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

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Answer 1 · 2015-10-02T22:24:59

$x=0.4$

To make things easy to write I'll call:

$log_(5)[0.8]=z$

So:

$5^z=2x$

Taking logs to base 5 of both sides $rArr$

$log_(5)5^z=log_(5)2x$

$zlog_(5)5=log_(5)2x$

Since $5^1=5:$

$log_(5)5=1$

So:

$zcancel(log_(5))5=log_(5)2x$

$z=log_(5)2x$

So:

$log_(5)[0.8]=log_(5)2x$

So:

$0.8=2x$

$x=0.4$

How do you solve for x 5^(log_5 *8) = 2x5^(log_5 *8) = 2x?