# Rearranging a Logarithm Functon

• SHRock
In summary, a logarithm function is the inverse of an exponential function and is used to solve equations with variables in the exponent. Rearranging a logarithm function can simplify complex equations and aid in graphing. This can be done by applying logarithm properties and algebraic techniques. Common mistakes include incorrect application of properties and errors in distribution, factoring, and isolating variables. Any type of logarithm function can be rearranged using the same techniques.
SHRock

y=ae^x

## Homework Equations

rearrange to find a

## The Attempt at a Solution

y/a=e^x

x=ln(y/a)

x=lny-lna

lny-x=lna

now how do I rearrange/inverse to seclude a

$$ln(y)-x = ln(a) \Rightarrow\; a = e^{ln(y)}e^{-x} = ye^{-x}$$

## What is a logarithm function?

A logarithm function is the inverse of an exponential function. It is used to solve equations in which the variable is in the exponent.

## Why would you need to rearrange a logarithm function?

Rearranging a logarithm function can help simplify complex equations and make them easier to solve. It can also help in graphing a logarithm function.

## How do you rearrange a logarithm function?

To rearrange a logarithm function, you can use the properties of logarithms such as the product, quotient, and power rules. You can also use algebraic techniques such as distributing, factoring, and isolating variables.

## What are some common mistakes when rearranging a logarithm function?

Some common mistakes when rearranging a logarithm function include forgetting to apply the logarithm properties correctly, not distributing or factoring correctly, and not isolating the variable in the logarithm expression.

## Can you rearrange any type of logarithm function?

Yes, you can rearrange any type of logarithm function, including natural logarithms (ln) and common logarithms (log). The same logarithm properties and algebraic techniques can be applied to any type of logarithm function.

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