Determining the value of a power

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To find the value of x in the equation y = z^x, use the logarithm: x = log(z) y, which expresses x as the logarithm of y with base z. However, this method may not yield correct results in all cases, particularly when using calculators that default to base 10 logarithms. For example, log(96059601) using base 10 does not return the expected exponent of 4 for 99^4. To accurately compute logarithms with different bases, one can either change the base manually or use a change of base formula. Understanding these logarithmic properties is essential for solving exponential equations effectively.
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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.
 
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Werg22 said:
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.
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.
 
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 I am not sure.

PS.Google is the best calculator ever
 
eNathan said:
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 I am not sure.

PS.Google is the best calculator ever
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).
 
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.
 
We know how to compute natural logarithms by hand...And from there,a change of basis implies another multiplication/division...

Daniel.
 

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