`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` .