Question 197260
{{{2^(5x)=8^(x+6)}}} Start with the given equation.



{{{2^(5x)=(2^3)^(x+6)}}} Rewrite {{{8}}} as {{{2^3}}}



{{{2^(5x)=2^(3(x+6))}}} Multiply the exponents.



{{{5x=3(x+6)}}} Since the bases are equal, this means that the exponents are equal.



{{{5x=3x+18}}} Distribute.



{{{5x-3x=18}}} Subtract {{{3x}}} from both sides.



{{{2x=18}}} Combine like terms on the left side.



{{{x=(18)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=9}}} Reduce.



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Answer:


So the solution is {{{x=9}}}