If log5 x - log5(x - 2) = 3, then the value of x, to the nearest hundredth, is?

Jan 13, 2017

$x \cong 2.02$ (Assuming $\log 5$ represents ${\log}_{5}$)

Explanation:

Assuming $\log 5$ represents ${\log}_{5}$ (log to the base 5), we have:

${\log}_{5} x - {\log}_{5} \left(x - 2\right) = 3$

${\log}_{5} \left(\frac{x}{x - 2}\right) = 3$

$\frac{x}{x - 2} = {5}^{3} = 125$

$x = 125 \left(x - 2\right)$

$124 x = 250$

$x = \frac{250}{124} \cong 2.02$ (To the nearest hundredth as requested)

However, to perform a check you should use 8 decimal places:
$x \cong 2.01612903$