Using Logarithms with Exponents

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Math › Using Logarithms with Exponents

Questions 1 - 4

1

Solve for

Explanation

Use the power reducing theorem:

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

and

$x\log 2 = 6$

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

2

Which of the following expressions is equivalent to ?

Explanation

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

3

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

Cannot be found by hand

Explanation

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

4

Simplify the expression below.

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

Explanation

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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