Question 932172

{{{3^(2x)=125}}}

{{{3^(2x)=5^3}}}...use log

{{{log(3^(2x))=log(5^3)}}}

{{{(2x)log(3)=3log(5)}}}

{{{x=(3/2)log(5)/log(3)}}}

{{{x=(3/2)log(5)/log(3)}}}  ...in base {{{10}}}, {{{log(5)=0.69897}}} and {{{log(3)=0.4771212547}}} approximately (because exact value is to long)

{{{x=(1.5)(0.69897/0.4771212547)}}}

{{{x=(1.5)(1.464973512)}}}

{{{x=2.197460268}}}  

{{{x=2.197460268}}}

check:

{{{3^(2*2.197460268)=124.999996}}}, rounded to whole number it is {{{125}}}