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

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`8^(x-1)=32^(3x-2)`

To solve, factor 8 and 32.

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

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...

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`8^(x-1)=32^(3x-2)`

To solve, factor 8 and 32.

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

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.

`3x-3=15x-10`

`3x-15x=3-10`

`-12x = -7`

`x=7/12`

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

Approved by eNotes Editorial Team