If `9^(2x+1) = (81^(x+2))/3^x` what is x?

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lemjay | High School Teacher | (Level 2) Senior Educator

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Since 9=3^2 and 81=3^4, express the equation with same base.


Apply the exponent property `(a^m)^n=a(^m*n)` .



Then at the right side of the equation, apply the property `a^m/a^n=a^m-n` .



Since both sides have the same base, to solve for x, equate the exponents equal to each other.






Hence, the solution to the given equation is `x=6` .

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