SOLUTION: Let 2^a = 5 and 2^b = 9. Using exponent rules, solve the equation in terms of a and/or b. 5^x=32 I really don't even know what the question is asking me to do. Please help!

Question 275351: Let 2^a = 5 and 2^b = 9. Using exponent rules, solve the equation in terms of a and/or b.
5^x=32
I really don't even know what the question is asking me to do. Please help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The goal here is to solve for 'x' in terms of either 'a' or 'b' (or both). In other words, have a solution of x = (something with 'a's and/or 'b's in it)

You have to play with it a bit, but it turns out that we never use . So let's just work with

First convert into logarithmic form to get . Now use the change of base formula to get

Now move onto and convert that into logarithmic form to get . Rewrite 32 as to get

Now pull down the exponent to get and use the change of base formula: . Take note how this is very similar to but this just has the reverse of that expression and an extra '5' in there. If we invert 'a', we then get which is the missing piece.

So

So the solution, in terms of 'a', is
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