Question 198963
{{{3^(x)*3^(x+1)*3^(x-2)=243}}} Start with the given equation.



{{{3^(x+x+1)*3^(x-2)=243}}} Multiply the first two terms using the identity {{{x^(y)*x^(z)=x^(y+z)}}}



{{{3^(2x+1)*3^(x-2)=243}}} Combine like terms.



{{{3^(2x+1+x-2)=243}}} Multiply the remaining terms using the identity {{{x^(y)*x^(z)=x^(y+z)}}}



{{{3^(3x-1)=243}}} Combine like terms.



{{{3^(3x-1)=3^5}}} Rewrite 243 as {{{3^5}}}



{{{3x-1=5}}} Since the bases are equal, this means that the exponents are equal.



{{{3x=5+1}}} Add {{{1}}} to both sides.



{{{3x=6}}} Combine like terms on the right side.



{{{x=(6)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.



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Answer:


So the solution is {{{x=2}}}