`8^(x-1)=32^(3x-2)` Solve the equation.

Expert Answers

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To solve, factor 8 and 32.


To simplify each side, apply the exponent rule `(a^m)^n = a^(m*n)` .

`2^(3*(x-1)) = 2^(5*(3x-2))`

`2^(3x-3) = 2^(15x-10)`

Since both sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right.



`-12x = -7`


Therefore, the solution is `x=7/12` .

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