# Whats the answer to log(x-1) = -1 ?

$x = 1.1$

#### Explanation:

Given that
$\setminus \log \left(x - 1\right) = - 1$

Taking Antilog on both the sides

$\setminus \textrm{A n t i \log} \left(\setminus \log \left(x - 1\right)\right) = \setminus \textrm{A n t i \log} \left(- 1\right)$

$x - 1 = {10}^{- 1}$

$x - 1 = \setminus \frac{1}{10}$

$x = 1 + \setminus \frac{1}{10}$

$x = \setminus \frac{11}{10}$

$x = 1.1$

Jun 21, 2018

$x = \frac{11}{10}$

#### Explanation:

The key realization is that if we have a logarithm of the form

${\log}_{b} a = x$, that this is equal to

${b}^{x} = a$

NOTE: If there's no base on the logarithm, it is implicitly base-10.

This means we can rewrite our logarithm as

${10}^{- 1} = x - 1$

Which simplifies to

$\frac{1}{10} = x - 1$

Adding $1$ to both sides, we get

$x = \frac{11}{10}$

Hope this helps!