Question 243551
{{{256^(x)= 64^(x+4)}}} Start with the given equation.



{{{(2^8)^(x)= (2^6)^(x+4)}}} Rewrite 256 as {{{2^8}}} and 64 as {{{2^6}}}



{{{2^(8x)= 2^(6(x+4))}}} Multiply the exponents.



{{{8x=6(x+4)}}} Since the bases are equal, the exponents are equal.



{{{8x=6x+24}}} Distribute.



{{{8x-6x=24}}} Subtract {{{6x}}} from both sides.



{{{2x=24}}} Combine like terms on the left side.



{{{x=(24)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=12}}} Reduce.



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Answer:


So the solution is {{{x=12}}}