Question 155813
{{{6*6^(3x)=36*6^x}}} Start with the given equation



{{{6^1*6^(3x)=36*6^x}}} Rewrite {{{6}}} as {{{6^1}}}



{{{6^1*6^(3x)=6^2*6^x}}} Rewrite {{{36}}} as {{{6^2}}}



{{{6^(1+3x)=6^(2+x)}}} Multiply the monomials by adding the exponents.



Since the bases are equal, this means that the exponents are equal. So this means that {{{1+3x=2+x}}}



{{{1+3x=2+x}}} Set the exponents equal to one another



{{{3x=2+x-1}}} Subtract {{{1}}} from both sides.



{{{3x-x=2-1}}} Subtract {{{x}}} from both sides.



{{{2x=2-1}}} Combine like terms on the left side.



{{{2x=1}}} Combine like terms on the right side.



{{{x=(1)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



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Answer:


So the answer is {{{x=1/2}}} which in decimal form is {{{x=0.5}}}.