# Understanding Logarithmic Function Problems: Solving for x

• feiser
In summary, a logarithmic function is the inverse of an exponential function, represented by the equation y = log<sub>b</sub>(x). It is used to solve exponential equations and has various applications in fields such as science, engineering, and finance. To solve logarithmic function problems, one can use the properties of logarithms, the change of base formula, or a calculator. Common mistakes to avoid include forgetting to simplify expressions, using the wrong base, and not checking for extraneous solutions. Logarithmic functions and exponential functions are inverses of each other and are used to solve equations in both directions.
feiser

## Homework Statement

solve x.
Log(35-x^3)/Log(5-x)=3

## Homework Equations

Log(a/b)=Log a - Log b

## The Attempt at a Solution

The answers would be 3 or 2
(so I'm guessing it has sumthing to do with quadratics)
i tried to expand the left side first, then rearrange it to Log(7/x^4)=3
the problem is that's not giving me the answer, which i got was 0.28925076.

Last edited:
The relevant equations you gave aren't necessary for the problem.
Move the Log(5-x) to the right hand side, then eliminate the logarithms. Then its just an algebra problem.

Thanks.

## What is a logarithmic function?

A logarithmic function is the inverse of an exponential function. It is represented by the equation y = logb(x), where b is the base of the logarithm. It is used to solve exponential equations and is commonly used in fields such as science, engineering, and finance.

## How do you solve logarithmic function problems?

To solve a logarithmic function problem, you can use the properties of logarithms, such as the product, quotient, and power rules. You can also use the change of base formula to convert logarithms with different bases into the same base, making it easier to solve. Additionally, you can use a calculator or a logarithmic table to solve more complex logarithmic functions.

## What are some common applications of logarithmic functions?

Logarithmic functions are used in a variety of fields, such as population growth, radioactive decay, sound and light intensity, and financial growth and decay. They are also used in measuring the pH scale, sound intensity, earthquake magnitude, and the Richter scale.

## What are the common mistakes to avoid when solving logarithmic function problems?

One common mistake is forgetting to simplify the expression before solving or using the wrong base when applying the logarithmic rules. It is also important to check for extraneous solutions, which can result from taking the logarithm of a negative number. Another mistake is not using parentheses when taking the logarithm of a complex expression, which can result in incorrect answers.

## How do logarithmic functions relate to exponential functions?

Logarithmic functions and exponential functions are inverses of each other. This means that the graph of a logarithmic function is a reflection of the graph of the corresponding exponential function over the line y = x. Additionally, logarithmic functions are used to solve exponential equations and vice versa.

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