Question 376321
{{{3^(4x-5)=9^(7x)}}} Start with the given equation.



{{{3^(4x-5)=(3^2)^(7x)}}} Rewrite 9 as {{{3^2}}}



{{{3^(4x-5)=3^(14x)}}} Multiply the exponents.



{{{4x-5=14x}}} Since the bases are equal, the exponents are equal.



{{{4x=14x+5}}} Add {{{5}}} to both sides.



{{{4x-14x=5}}} Subtract {{{14x}}} from both sides.



{{{-10x=5}}} Combine like terms on the left side.



{{{x=(5)/(-10)}}} Divide both sides by {{{-10}}} to isolate {{{x}}}.



{{{x=-1/2}}} Reduce.



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Answer:


So the solution is {{{x=-1/2}}}



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