Express Exponential Models as Logarithmic Solutions: CCSS.Math.Content.HSF-LE.A.4 - Common Core: High School - Functions

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Question

Solve for using rules of logarithmic functions.

$e^{x-4}+2=10$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$e^{x-4}+2=10$

Subtract two from both sides.

$\e^{x-4}+2-2=10-2 \e^{x-4}=8$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^{x-4}=8 \ \ln e^{x-4}=\ln 8\ x-4=\ln 8\x=\ln 8+4$

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Question

Solve for using rules of logarithmic functions.

$e^{x-4}+1=5$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$e^{x-4}+1=5$

Subtract one from both sides.

$\e^{x-4}+1-1=5-1 \e^{x-4}=4$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^{x-4}=4 \ \ln e^{x-4}=\ln 4\ x-4=\ln 4\x=\ln 4+4$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$2e^{x}+1=5$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$2e^{x}+1=5$

Subtract one from both sides.

$\2e^{x}+1-1=5-1 \2e^{x}=4$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\2e^x=4 \e^x=\frac{4}{2} \ \e^x=2 \ \ln e^x=\ln2 \x=\ln 2$

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Question

Solve for using rules of logarithmic functions.

$2e^{x}+5=17$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$2e^{x}+5=17$

Subtract five from both sides and then divide by two.

$\2e^{x}+5-5=17-5\2e^{x}=12\e^x=6$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^x=6 \ \ln e^x=\ln6 \x=\ln 6$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$4e^{x}+5=17$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$4e^{x}+5=17$

Subtract five from both sides and then divide by four.

$\4e^{x}+5-5=17-5\4e^{x}=12\e^x=3$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^x=3 \ \ln e^x=\ln3 \x=\ln 3$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$4e^{x}+5=13$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$4e^{x}+5=13$

Subtract five from both sides and then divide by four.

$\4e^{x}+5-5=13-5\4e^{x}=8\e^x=2$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^x=2 \ \ln e^x=\ln2 \x=\ln 2$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$4e^{x}-6=12$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$4e^{x}-6=12$

Add six from both sides and then divide by four.

$\4e^{x}-6+6=12+6\4e^{x}=18\\e^x=\frac{9}{2}$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^x=\frac{9}{2} \\ \ln e^x=\ln\frac{9}{2} \x=\ln \frac{9}{2}$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$e^{x-4}-2=10$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$e^{x-4}-2=10$

Add two from both sides.

$\e^{x-4}-2+2=10+2 \e^{x-4}=12$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^{x-4}=12 \ \ln e^{x-4}=\ln 12\ x-4=\ln 12\x=\ln 12+4$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$e^{x-4}-1=5$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$e^{x-4}-1=5$

Add one from both sides.

$\e^{x-4}-1+1=5+1 \e^{x-4}=6$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^{x-4}=6 \ \ln e^{x-4}=\ln 6\ x-4=\ln 6\x=\ln 6+4$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$e^{x-4}-1=1$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$e^{x-4}-1=1$

Add one from both sides.

$\e^{x-4}-1+1=1+1 \e^{x-4}=2$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$

Step 3: Apply logarithmic rules to solve for .

$\e^{x-4}=2 \ \ln e^{x-4}=\ln 2\ x-4=\ln 2\x=\ln 2+4$

Compare your answer with the correct one above

Question

Solve for using rules of logarithmic functions.

$e^{x-4}-1=0$

Answer

This question is testing one's ability to understand logarithmic rules and apply them in order to solve a function.

For the purpose of Common Core Standards, "For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and _d_are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.4).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Use algebraic operations to manipulate the function and isolate the value on one side of the equation.

$e^{x-4}-1=0$

Add one from both sides.

$\e^{x-4}-1+1=0+1 \e^{x-4}=1$

Step 2: Identify logarithmic rules.

Recall that $\ln e=1$ and $\ln1=0$

Step 3: Apply logarithmic rules to solve for .

$\e^{x-4}=1 \ \ln e^{x-4}=\ln 1\ x-4=\ln 1\x=\ln 1+4\x=0+4\x=4$

Compare your answer with the correct one above

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