What is the solution to x?

Question

9.207=9.389+log(x/0.0186186)

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Answer 1 · 2018-03-21T08:40:24

$x = 0.012246162 \approx 1.22 \cdot 10^{- 2}$ $x=0.012246162~~1.22*10^-2$

Given: $9.207 = 9.389 + log (\frac{x}{0.0186186})$ $9.207=9.389+log(x/0.0186186)$

We subtract $9.389$ $9.389$ from both sides and get,

$log (\frac{x}{0.0186186}) = - 0.182$ $log(x/0.0186186)=-0.182$

Using logarithm properties, $log (\frac{x}{0.0186186}) = log x - log (0.0186186)$ $log(x/0.0186186)=logx-log(0.0186186)$ , and so we get,

$log x - log (0.0186186) = - 0.182$ $logx-log(0.0186186)=-0.182$

$log x = log (0.0186186) - 0.182$ $logx=log(0.0186186)-0.182$

$log x = - 1.73 - 0.182$ $logx=-1.73-0.182$

$log x = - 1.912$ $logx=-1.912$

$x = 10^{- 1.912}$ $x=10^-1.912$

$= 0.012246162$ $=0.012246162$

Answer 2 · 2018-03-21T08:41:03

Here's what I got.

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