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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.
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