Question 92951
{{{5^(x-1) = 125^(2x+3)}}}



{{{5^(x-1) = (5^3)^(2x+3)}}} Rewrite 125 as {{{5^3}}}


{{{5^(x-1) = 5^(3(2x+3))}}} Multiply the exponents


{{{5^(x-1) = 5^(6x+9)}}} Distribute



Now that we have the same base, we can set the exponents equal to each other



{{{x-1=6x+9}}}



{{{x=6x+9+1}}} Add 1 to both sides



{{{x-6x=9+1}}} Subtract 6x from both sides




{{{-5 x=9+1}}} Combine like terms {{{1 x}}} and {{{-6 x}}} on the left side to get {{{-5 x}}}





{{{-5 x=10}}} Combine like terms 1 and 9 on the right side to get 10






{{{x=(10)/(-5)}}} Now divide both sides by  -5 to isolate and solve for x



{{{x= -2}}} Reduce




So our answer is

{{{x= -2}}}



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Check:


{{{5^(-2-1) = 125^(2(-2)+3)}}} Plug in {{{x= -2}}} into the original equation


{{{5^(-2-1) = 125^(-4+3)}}} Multiply


{{{5^(-3) = 125^(-1)}}} Combine like terms in the exponents


{{{1/5^3 = 1/125}}} Rewrite {{{125^(-1)}}} as {{{1/125^1}}} which is just  {{{1/125}}}. Rewrite {{{5^(-3)}}} as {{{1/5^3}}}


{{{1/125 = 1/125}}} Evaluate {{{1/5^3}}} to get {{{1/125}}}. Since the equations are equal, our answer is verified.