# How To Solve Logarithmic Problems

Since log problems are typically simpler, I'll start with them.wiki How is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. Once you rewrite the logarithm into a more familiar form, you should be able to solve it as you would solve any standard exponential equation.Don’t forget that when using the square root property, both positive and negative roots must be considered. There are several strategies that can be used to solve equations involving exponents and logarithms.

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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.

In these cases, you need to complete a few more steps in solving for the variable. In this case, divide both sides by 3, then use the square root property to find the possible values for x.

In this section we will now take a look at solving logarithmic equations, or equations with logarithms in them.

We will be looking at two specific types of equations here.

As you know, algebra often requires you to solve equations to find unknown values.

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.

In this case we will use the fact that, \[x = yx = y\] In other words, if we’ve got two logs in the problem, one on either side of an equal sign and both with a coefficient of one, then we can just drop the logarithms. With this equation there are only two logarithms in the equation so it’s easy to get on one either side of the equal sign.

We will also need to deal with the coefficient in front of the first term.

## Comments How To Solve Logarithmic Problems

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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.…

• ###### Ways to Solve Logarithms - wikiHow

How to Solve Logarithms - Solve for X Using the Logarithmic Product Rule34 Know the product rule. Isolate the logarithm to one side of the equation. Apply the product rule. Rewrite the equation in exponential form. Solve for x. Write your answer.…

• ###### Solving Log Equations - Cool Math

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• ###### Solving Log Equations with Exponentials Purplemath

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• ###### 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 - 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.…