Determining the value of a power

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Discussion Overview

The discussion revolves around determining the value of the exponent \( x \) in the equation \( y = z^x \) in terms of \( y \) and \( z \). Participants explore mathematical relationships, particularly focusing on logarithmic functions and their properties.

Discussion Character

  • Mathematical reasoning
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant asks how to express \( x \) as a function of \( y \) and \( z \) in the equation \( y = z^x \).
  • Another participant suggests that the inverse relation is the logarithm in base \( z \), stating that \( x = \log_z(y) \) and references properties of logarithms.
  • Some participants discuss specific examples, noting that while \( \log(1000) = 3 \) works correctly, \( \log(96059601) \) does not yield the expected exponent when using base 10 logarithms.
  • It is mentioned that the discrepancy arises because calculators typically use base 10 logarithms, and a change of base is necessary to obtain the correct exponent.
  • One participant expresses a belief that there should be a general equation to calculate the power for any logarithmic base.
  • Another participant notes the method for computing natural logarithms and implies that a change of base involves additional multiplication or division.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single method for calculating the exponent \( x \) across different bases, and there are varying opinions on the effectiveness of logarithmic functions in different scenarios.

Contextual Notes

Participants highlight limitations related to the use of different logarithmic bases and the potential for confusion when using calculators that default to base 10.

Werg22
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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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