SOLUTION: Please help with this equation: log(base a) 5 = -3/4

Question 267671: Please help with this equation:
log(base a) 5 = -3/4
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Eventually we want an equation that says
a = some-number
So we need to get the "a" out of the base of the logarithm. We can so this by rewriting the equation in exponential form:

Now we need to change the exponent on "a" to a 1 (because ). The quickest way to do this make clever use of the rules for exponents. I am going to raise both sides of the equation to the -4/3 power. (See what happens to see why.)

On the right side, the rule is to multiply the exponents. And what do you get when you multiply -3/4 and -4/3? Answer: 1!

This may be an acceptable answer. If you want a decimal approximation you can use your calculator on the expression on the left side. Or, for an exact answer with rational denominators...

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