How do you solve $log (\frac{1}{x}) = 7.761$ $log(1/x)=7.761$ ?

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Answer 1 · 2016-01-02T10:11:09

By simply solving with the exponential form.

$x = 0.12885$ $x=0.12885$

$log (\frac{1}{x}) = 7.761$ $log(1/x)=7.761$

Supposing that the base is 10:

$log (\frac{1}{x}) = {log 10}^{7.761}$ $log(1/x)=log10^7.761$

Since $log$ $log$ is a 1-1 function for $x > 0$ $x>0$ and $x \neq 1$ $x!=1$ the $log$ $log$ can be cancelled out:

$\frac{1}{x} = 10^{7.761}$ $1/x=10^7.761$

$x = \frac{1}{10^{7.761}} = 10^{- 7.761} = 0.12885$ $x=1/10^7.761=10^-7.761=0.12885$

How do you solve log(1x)=7.761log(1/x)=7.761?