Determining the value of a power

In summary, there is a mathematical relationship between y and x in the equation y=z^x, which can be solved using the inverse relation of logarithms in base z. However, this method may not work for all situations and may require additional calculations.
  • #1
Werg22
1,431
1
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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  • #2
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.
 
  • #3
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
 
  • #4
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).
 
  • #5
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
We know how to compute natural logarithms by hand...And from there,a change of basis implies another multiplication/division...

Daniel.
 

What is a power?

A power is a mathematical operation that involves raising a number to a certain exponent.

How do you determine the value of a power?

The value of a power can be determined by multiplying the base number by itself the number of times indicated by the exponent. For example, 23 would be calculated as 2 x 2 x 2, resulting in a value of 8.

What is the base number in a power?

The base number is the number that is being raised to a certain power. It is the number that is multiplied by itself the number of times indicated by the exponent.

What is an exponent?

An exponent is a number that indicates how many times the base number should be multiplied by itself in a power operation. It is represented by a superscript number above the base number.

Can a power have a negative exponent?

Yes, a power can have a negative exponent. This indicates that the base number should be divided by itself the number of times indicated by the exponent. For example, 2-3 would be calculated as 1 / (2 x 2 x 2), resulting in a value of 1/8 or 0.125.

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