How do you use log to verify that 10 = 5 * 2 ?

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Answer 1 · 2018-06-25T11:51:36

Given $10 = 5 \cdot 2$ $10=5·2$ we take log in both sides. Then we have

$log 10 = log (5 \cdot 2) = log 5 + log 2$ $log10=log(5·2)=log5+log2$ by log rules

$log 10 = 1$ $log10=1$ because allways ${log}_{b} b = 1$ $log_b b=1$

Now use a calculator to find $log 5$ $log5$ and $log 2$ $log2$

$log 5 = 0.6989700043$ $log5=0.6989700043$
$log 2 = 0.30102999957$ $log2=0.30102999957$

The sum of both numbers have to be 1. Lets check

$0.6989700043 + 0.30102999957 = 1$ $0.6989700043+0.30102999957=1$