How do you solve log(x+1) = 2 + log x?

Dec 1, 2015

$x = \frac{1}{99}$

Explanation:

Know that: $\left\{\begin{matrix}\log a - \log b = \log \left(\frac{a}{b}\right) \\ \log a = b \iff a = {10}^{b}\end{matrix}\right.$

$\log \left(x + 1\right) = 2 + \log x$

$\log \left(x + 1\right) - \log x = 2$

$\log \left(\frac{x + 1}{x}\right) = 2$

$\frac{x + 1}{x} = {10}^{2}$

$x + 1 = 100 x$

$x = \frac{1}{99}$