# Solve the equation 5^x=4^(x+1)?

Mar 5, 2017

$x = 6.213$

#### Explanation:

As ${5}^{x} = {4}^{x + 1}$, taking logarithm on both sides we get

$x \log 5 = \left(x + 1\right) \log 4$

or $x \left(\log 5 - \log 4\right) = \log 4$

or $x = \log \frac{4}{\log 5 - \log 4}$

or $x = \log \frac{4}{\log} \left(\frac{5}{4}\right)$

or $x = \log \frac{4}{\log} 1.25 = \frac{0.60206}{0.09691} = 6.213$