Converting a log equation to exponential equation

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SUMMARY

The discussion centers on converting the logarithmic equation f(x) = log5(x) + 3 into its exponential form. The exponential equivalent is derived as x = 5^(y - 3), which simplifies to x = (1/125) * 5^y. This transformation utilizes the properties of logarithms and exponents, specifically the definition of logarithms as the inverse of exponential functions. The participants confirm the correct approach to graphing and solving the equation.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with exponential functions and their inverses
  • Basic algebraic manipulation skills
  • Knowledge of graphing functions
NEXT STEPS
  • Study the properties of logarithms and their inverses
  • Learn how to graph exponential functions
  • Explore the relationship between logarithmic and exponential equations
  • Practice solving equations involving logarithms and exponents
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Students studying algebra, educators teaching logarithmic and exponential functions, and anyone looking to deepen their understanding of mathematical transformations.

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Homework Statement


the question asks to graph the equation:
(don't know how to use latex sorry)
f(x) = log5 (x) + 3 where the 5 is the base
Just for my curiosity what would the exponential equation be?
I can graph it, just can't get the exponential form
Tell me if this should go in the general math section.
 
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You already put it in the general math section lol, look there for the working.
5^{f(x)} = 125x
 
Can that be expressed as x=? and can you show me how you did that?
 
wScott said:

Homework Statement


the question asks to graph the equation:
(don't know how to use latex sorry)
f(x) = log5 (x) + 3 where the 5 is the base
Just for my curiosity what would the exponential equation be?
I can graph it, just can't get the exponential form
Tell me if this should go in the general math section.

"Solve" for x: y- 3= log5(x) so, using the definition of log5(x) as the inverse of 5x, x= 5y-3= (1/125)5y.
 

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