# How do you solve for x 5^(log_5 *8) = 2x?

Oct 2, 2015

$x = 0.4$

#### Explanation:

To make things easy to write I'll call:

${\log}_{5} \left[0.8\right] = z$

So:

${5}^{z} = 2 x$

Taking logs to base 5 of both sides$\Rightarrow$

${\log}_{5} {5}^{z} = {\log}_{5} 2 x$

$z {\log}_{5} 5 = {\log}_{5} 2 x$

Since ${5}^{1} = 5 :$

${\log}_{5} 5 = 1$

So:

$z \cancel{{\log}_{5}} 5 = {\log}_{5} 2 x$

$z = {\log}_{5} 2 x$

So:

${\log}_{5} \left[0.8\right] = {\log}_{5} 2 x$

So:

$0.8 = 2 x$

$x = 0.4$