Using Logarithms with Exponents - High School Math

Card 0 of 4

Question

Evaluate by hand $\log_2(4^{\log_2(4^{5})})$

Answer

Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as $5\log_2(4)\log_2(4)$

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Question

Solve for

Answer

Use the power reducing theorem:

$\log a^x = b \rightarrow x\log a = b$

and

$x\log 2 = 6$

$x= \frac{6}{\log 2}$

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Question

Which of the following expressions is equivalent to ?

Answer

According to the rule for exponents of logarithms,. As a direct application of this,.

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Question

Simplify the expression below.

$log(2 \cdot 2 \cdot 2)$

Answer

Based on the definition of exponents, $log(2 \cdot 2 \cdot 2) = log (2^{3})$ .

Then, we use the following rule of logarithms:

$log(m^{n}) = n\cdot log(m)$

Thus, $log(2^{3}) = 3log(2)$ .

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