SOLUTION: log (base 2) 40 = x

Question 267919: log (base 2) 40 = x
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

There is no calculator I know of which can calculate base 2 logarithms. So how do we figure this out? Answer: We have to change the base to one our calculator "knows", like base 10 or base e (ln) logarithms. There is a formula for this but I always have trouble remembering it. So here's how I would do this problem. First, I'll rewrite the equation in exponential form:

Now we'll find the base 10 (or base e) logarithm of each side:

Next I'll use the property of logarithms, , to move the exponent out in front:

Now I'll divide both sides by log(2):

Note 1: This is what you would have gotten if you used the base conversion formula for logarithms.
Note 2: If you used base e logarithms you would have:

and, believe it or not, you will get the same answer from both equations.
Note 3: log(40)/log(2) IS NOT log(20)!!

Now just use your calculator to find the two logarithms and divide. You should get something close to 5.322.

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