Question 151075
{{{4^(2x-3) = 1/16}}} Start with the given equation.



{{{(2^2)^(2x-3) = 1/16}}} Rewrite {{{4}}} as {{{2^2}}}



{{{2^(2(2x-3)) = 1/16}}} Multiply the exponents.



{{{2^(2(2x-3)) = 2^(-4)}}} Rewrite {{{1/16}}} as {{{16^(-1)=(2^4)^(-1)=2^((4)(-1))=2^(-4)}}}



{{{2(2x-3)=-4}}} Since the bases are equal, this means that the exponents are equal.



{{{4x-6=-4}}} Distribute.



{{{4x=-4+6}}} Add {{{6}}} to both sides.



{{{4x=2}}} Combine like terms on the right side.



{{{x=(2)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}.



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



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Answer:


So the answer is {{{x=1/2}}} 



Which approximates to {{{x=0.5}}}