# SOLUTION: 8^(3x-2)=64

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 Question 250492: 8^(3x-2)=64Answer by jsmallt9(3438)   (Show Source): You can put this solution on YOUR website! The simplest solution is found by recognizing that 64 is a power of 8. So we can rewrite the equation as: Since both sides are results of raising 8 to a power, the exponents must be equal: Solving this: If we don't notice that we can solve this using logarithms. We can use any base of logarithm. But we should pick a base our calculator can find. So I will use base 10: Now we can use a property of logarithms, , to move the exponent of the argument out in front. (This is the reason we use logarithms on problems like this: to get the variable out of the exponent.) Now we solve for x. Divide both sides by : Add 2 to each side: Multiply both sides by 1/3: If we enter the expression on the right into our calculator we end up with x = 1.333333... which is 4/3 in decimal form.