Logging

Algebra Level 2

What is the value of x in the following equation:
log ⁡ 8 216 − log ⁡ 8 27 = log ⁡ 2 x \large\log_{8}216-\log_{8}27= \log_{2}x


The answer is 2.

Kenny O. by Kenny O. , 17, Singapore

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2 solutions

Kenny O.
Dec 1, 2017

l o g 8 log_8 216- l o g 8 log_8 27= l o g 8 log_8 216 27 \frac{216}{27} = l o g 8 log_8 8=1.
l o g 2 log_2 x=1. => 2 1 = x 2^1=x . x=2

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By the laws of logarithm,

log ⁡ 8 216 − log ⁡ 8 27 = log ⁡ 8 216 27 = log ⁡ 8 8 = 1 \log_{8}216 -\log_{8}27=\log_{8}\dfrac{216}{27}=\log_{8}8=1

⟹ log ⁡ 2 x = 1 \implies \log_{2}x=1

⟹ x = 2 \implies \boxed{x=2}

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