Question 926367
{{{3^(2x-1) = 5^(x+4)}}}


{{{3^(2x)/3 = 5^(x+4)}}}

{{{(3^2)^x)= 3*5^(x+4)}}}


{{{9^x= 3*5^(x+4)}}}.....use logarithm

{{{log(9^x)= log(3*5^(x+4))}}}

{{{x*log(9)= log(3*5^(x+4))}}}

{{{x= log(3*5^(x+4))/log(9)}}}

{{{x= (log(3)+log(5^(x+4)))/log(3^2)}}}

{{{x= (log(3)+(x+4)(log(5)/2log(3)))}}}

{{{x= log(3)/2log(3)+(x+4)(log(5)/2log(3))}}}

{{{x= 1/2 +(x+4)(log(5)/2log(3))}}}

{{{x =1/2+(x+4)(log(5)/2log(3))}}}........{{{0.732486760358963583598520203839320198153966183333024844526445=log(5)/2log(3)}}} or round it to {{{0.73248676 =log(5)/2log(3)}}}


{{{x=1/2+0.73248676(x+4)}}}


{{{x=0.5+0.73248676x+2.92994704}}}


{{{x-0.73248676x=0.5+2.92994704}}}


{{{(1-0.73248676)x=0.5+2.92994704}}}


{{{(0.26751324)x=3.42994704}}}


{{{x=3.42994704/0.26751324}}}


{{{x=12.8216}}}


check:

{{{3^(2x-1) = 5^(x+4)}}}

{{{3^(25.6432-1) = 5^(12.8216+4)}}}

{{{3^(24.6432) = 5^(16.8216)}}}

{{{5.72525 *10^11=5.72524* 10^11}}}

{{{5.73*10^11=5.73*10^11}}}