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How do you solve $5^{2 x} = 8$ $5^(2x) = 8$ ?

1 Answer

May 13, 2016

$x = \frac{{log}_{5} 8}{2} \approx 0.646$ $x=color(blue)((log_5 8)/2)~~color(blue)(0.646)$

Explanation:

If $5^{2 x} = 8$ $5^(2x) = 8$
then
$XXX {log}_{5} 5^{2 x} = {log}_{5} 8$ $color(white)("XXX")log_5 5^(2x)=log_5 8$

$XXX \to 2 x = {log}_{5} 8$ $color(white)("XXX")rarr 2x=log_5 8$

$XXX \to x = \frac{{log}_{5} 8}{2}$ $color(white)("XXX")rarr x= (log_5 8)/2$

Use a calculator to obtain an approximate value for this expression.

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