Question

4 evaluate each expression:
a) $log_{2} 16 = $
b) $log_{25} 5 = $
c) $log_{3} \frac{1}{27} = $
d) $log_{4} 256 = $

Explanation:

Step1: Rewrite 16 as power of 2

$\log_{2}16 = \log_{2}2^4$

Step2: Apply log power rule

$\log_{2}2^4 = 4\log_{2}2 = 4$
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Step1: Rewrite 5 as power of 25

$\log_{25}5 = \log_{25}25^{\frac{1}{2}}$

Step2: Apply log power rule

$\log_{25}25^{\frac{1}{2}} = \frac{1}{2}\log_{25}25 = \frac{1}{2}$
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Step1: Rewrite $\frac{1}{27}$ as power of 3

$\log_{3}\frac{1}{27} = \log_{3}3^{-3}$

Step2: Apply log power rule

$\log_{3}3^{-3} = -3\log_{3}3 = -3$
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Step1: Rewrite 256 as power of 4

$\log_{4}256 = \log_{4}4^4$

Step2: Apply log power rule

$\log_{4}4^4 = 4\log_{4}4 = 4$

Answer:

A) $4$
B) $\frac{1}{2}$
C) $-3$
D) $4$