How do you solve 2^(x+1) = 3^x?

Jan 23, 2016

$x \approx 1.7093$

Explanation:

${2}^{x + 1} = {3}^{x}$
Taking log of both sides
$\log {2}^{x + 1} = \log {3}^{x}$
$\implies \left(x + 1\right) \log 2 = x \log 3$
$\implies \left(x + 1\right) \times 0.3010 = x \times 0.4771$
Rearranging we get
$\left(- 0.3010 + 0.4771\right) x = 0.3010$
$\implies x = \frac{0.3010}{0.4771 - 0.3010}$

$x \approx 1.7093$