If Logx (1 / 8) = - 3 / 2, then x is equal to?
We can apply the base-change rule on the left side so we have base 10 logs and the "x" is now inside a log instead of being a base of one: log(1/8) / log(x) = -3/2 Now we can multiply both sides by log(x) log(1/8) = -3 log(x) / 2 Now multiply both sides by -2/3 to get the log(x) by itself: -2/3 log(1/8) = log(x) If you are multiplying something by a log, it's the same as moving the coefficient inside the log as the exponent. You usually use this rule to move an exponent out, but in this case, we want it in: a log(x) = log(x^a) So now we have: log[(1/8)^(-2/3)] = log(x) Set both sides to be an exponent of a base of 10, which will remove the logs from both sides: x = (1/8)^(-2/3) Now, simplify this. First, resolve the negative exponent by taking the reciprocal of the base: x = 8^(2/3) Now change it to radical form since you have a fractional exponent: x = ³√(8)² You can take the cube root of 8: x = 2² And finally: x = 4
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