# Thread: exponential function

1. ## exponential function

I am having trouble solving with the following problem:

If 15^2x=4, what does 15^2x equal

How do you rewrite 15^2x=4 so x can be solved for without a calculator?

Any help is appreciated

2. ## Re: exponential function

Hey phasediagram.

Hint: 15^2x = (15^2)^x = 225^x = 4. Do you know about logarithms?

3. ## Re: exponential function

I am learning about logarithms now. i seem to be drawing a blank

4. ## Re: exponential function

With logarithms if a^x = y then log_a(y) = x where log_a is the logarithm to the base a. The common bases are the natural base e and base 10. To get any base you use the formula log_a(x) = log_b(x)/log_b(a) where log_b is the logarithm in base b and you use b = e (natural) or b = 10 where a is any base that is a whole number typically greater than 1 (but it can be in between 0 and 1 not including those two numbers).

5. ## Re: exponential function

got it! thanks

6. ## Re: exponential function

You can also proceed directly by taking log on both sides and you will get 2x log 15 = log 4
x = (1/2) [ (log 4 )/ ( log 15)] Now just plug in values of log and you will get the value of x