How do you solve for x in ${(125)}^{x} = 625$ $(125)^x = 625$ ?

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Answer 1 · 2016-04-09T05:49:27

$x = \frac{4}{3} = 1.333$ $x=4/3=1.333$

$125^{x} = 625$ $125^x=625$ means $x = {log}_{125} 625$ $x=log_(125)625$

As ${log}_{b} a = \frac{log a}{log b}$ $log_ba=loga/logb$

$x = \frac{log 625}{log 125} = \frac{2.79588}{2.09691} = 1.333$ $x=log625/log125=2.79588/2.09691=1.333$

Alternately - $125^{x} = 625 \Leftrightarrow {(5^{3})}^{x} = 5^{4} \Leftrightarrow 5^{3 x} = 5^{4}$ $125^x=625hArr(5^3)^x=5^4hArr5^(3x)=5^4$ or

$3 x log 5 = 4 log 5$ $3xlog5=4log5$ or $x = \frac{4}{3} = 1.333$ $x=4/3=1.333$

How do you solve for x in (125)^x = 625(125)x=625(125)^x = 625?