# Determining the value of a power

1. Apr 8, 2005

### Werg22

in an equation such as:

y=z^x

How to find out the value of x in function of y and z? I'm sure there is a mathematical relaionship... thank you in advance.

2. Apr 8, 2005

### hypermorphism

The inverse relation is the logarithm in base z. Ie., if y = zx, then x = logz y, read as "the log in base z of y". It may be helpful to look at the properties of logarithms (really just the ordinary properties of exponents), in particular the change of base formula.

3. Apr 9, 2005

### eNathan

ye, as hypermorphism said, just use Log() like this...

If y = z^x then x = log(z)

But this does not work for every situation. For isntance, if I have (givin y = z^x) 1000 = 10^3 then Log(1000) = 3 and it works fine.

But if I have 96059601 = 99^4 then Log(96059601) = 7.98254078 which does not result in the original '4', probally because the 99 is not taken into account im not sure.

PS.Google is the best calculator ever

4. Apr 9, 2005

### hypermorphism

That is because Log() on Google refers to Log10. In order to get 4, just use Log99, or if Google doesn't allow change of base, change the base yourself by dividing your base ten logarithm by Log10(99).

5. Apr 9, 2005

### Werg22

It doesn’t quite answer my question... there has to be an equation to calculate the power for any value of logarithms base. Google and every calculator have to calculate-it some how.

6. Apr 9, 2005

### dextercioby

We know how to compute natural logarithms by hand...And from there,a change of basis implies another multiplication/division...

Daniel.