*When the bases are the same, or the exponents are the same, you can just compare the parts that are different. Logarithmic equations may also involve inputs where the variable has a coefficient other than 1, or where the variable itself is squared.*

I start with the original equation and work with the "outer" log: You can use the Mathway widget below to practice solving logarithmic equations (or skip the widget and continue with the lesson).

Try the entered exercise, or type in your own exercise.

This will be important down the road and so we can’t forget that.

Now, let’s start off by looking at equations in which each term is a logarithm and all the bases on the logarithms are the same.

to solve equations using the change-of-base formula, or always by using the definition of logs, or any other particular method.

But I am suggesting that you should make sure that you're comfortable with the various methods, and that you shouldn't panic if you and a friend used I can't do anything with this equation yet, because I don't yet have it in the "log(of something) equals a number" form.

So I'll need to use log rules to combine the two terms on the left-hand side of the equation: Now the equation is arranged in a useful way.

At this point, I can use The Relationship to convert the log form of the equation to the corresponding exponential form, and then I can solve the result: Keep in mind that you can always check your answers to any "solving" exercise by plugging those answers back into the original equation and checking that the solution "works".

When you have solved other algebraic equations, you often relied on the idea that you can change both sides of the equation in the same way and still get a true equation.

This is true with logarithms, too: If x = y, then log Another kind of exponential equation has exponential expressions on both sides.

## Comments How To Solve Logarithmic Problems

## Logarithmic Equation Calculator - Symbolab

Free logarithmic equation calculator - solve logarithmic equations step-by-step. Limited Storage 10 problems Practice problems limited to one per topic…

## Logarithmic Word Problems - Purplemath

Logarithmic Word Problems page 1 of 3 Logarithmic word problems, in my experience, generally involve evaluating a given logarithmic equation at a given point, and solving for a given variable; they're pretty straightforward. On the other hand, exponential word problems tend to be much more involved, requiring.…

## Solving Log Equations - Cool Math

This algebra lesson shows explains how to solve log logarithmic equations Exponentials & Logarithms - Cool math Algebra Help Lessons - Solving Logarithmic Equations welcome to coolmath…

## Solving Logarithmic Equations - Practice Problems

Solving Logarithmic Equations – Practice Problems Move your mouse over the "Answer" to reveal the answer or click on the "Complete Solution" link to reveal all of the steps required to solve logarithmic equations.…

## Solving Log Equations with Exponentials Purplemath

You can use the Mathway widget below to practice solving logarithmic equations or skip the widget and continue with the lesson. Try the entered exercise, or type in your own exercise. Then click the button to compare your answer to Mathway's.…

## Solving Logarithmic Equations - ChiliMath

If you have a single logarithm on one side of the equation then you can express it as an exponential equation and solve. Let's learn how to solve logarithmic.…

## SOLVING LOGARITHMIC EQUATIONS

To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable. Example 1 Solve for x in the equation Lnx=8. Solution Step 1 Let both sides be exponents of the base e. The equation Lnx=8 can be rewritten.…

## How to Solve Logarithmic Equations - dummies

How to Solve Logarithmic Equations. You can combine all the logs so that you have one log on the left and one log on the right, and then you can drop the log from both sides. For example, to solve log 3 x – 1 – log 3 x + 4 = log 3 5, first apply the quotient rule to get.…

## Solving Logarithmic Equations - Mesa Community College

Steps for Solving Logarithmic Equations Containing Only Logarithms Step 1 Determine if the problem contains only logarithms. If so, go to Step 2. If not, stop and use the Steps for Solving Logarithmic Equations Containing Terms without Logarithms.…