Solve for x. `2^(x-1) = 31` Enter answer correct to four decimals.  

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`2^(x-1) = 31`

To solve, first remove the x in the exponent. To do so, take the logarithm of both sides.

`ln 2^(x-1)=ln31`

At the left side, apply the rule `ln a^m = mlna` .

`(x-1)ln2=ln31`

Then, divide both sides by ln2.

`((x-1)ln2)/(ln2)=(ln31)/(ln2)`

`x-1=(ln31)/(ln2)`

And, add both sides by 1.

`x-1+1=(ln31)/(ln2)+1`

`x=5.9542`

Hence, the solution to the equation is `x=5.9542` .

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