# Rewrite as a single logarithm and simplifying

Example 3: Combine or condense the following log expressions into a single logarithm: Start by applying Rule 2 Power Rule in reverse to take care of the constants or numbers on the left of the logs.

## Simplifying logarithms

I can put together that variable x and constant 2 inside a single parenthesis using division operation. So we can simplify. Rule 5: Identity Rule The logarithm of a number that is equal to its base is just 1. Remember that Power Rule brings down the exponent, so the opposite direction is to put it up. Properties of logarithms Video transcript We're asked to simplify log base 5 of 25 to the x power over y. So then we are left with, this is equal to-- and I'll write it in front of the x now-- 2 times x minus log base 5 of y. So we can use some logarithm properties. So this simplifies to 2. And we're done. Now, this looks like we can do a little bit of simplifying. And here we have 25 to the x over y.

Free Math Lessons, Videos, Quizzes and Worksheets Combining or Condensing Logarithms The reverse process of expanding logarithms is called combining or condensing logarithmic expressions into a single quantity.

Unnecessary errors can be prevented by being careful and methodical in every step. Description of Each Logarithm Rule Rule1: Product Rule The logarithm of the product of numbers is the sum of logarithms of individual numbers.

So we can use some logarithm properties.

This part right here is asking us, what power do I have to raise 5 to to get to 25? And this is useful because log base 5 of 25 is actually fairly easy to think about. Rule 7: Exponent of Log Rule Raising the logarithm of a number by its base equals the number.

### Rewrite as a single logarithm and simplifying

Rule 7: Exponent of Log Rule Raising the logarithm of a number by its base equals the number. Free Math Lessons, Videos, Quizzes and Worksheets Combining or Condensing Logarithms The reverse process of expanding logarithms is called combining or condensing logarithmic expressions into a single quantity. And then, of course, we have minus log base 5 of y. And this is useful because log base 5 of 25 is actually fairly easy to think about. So then we are left with, this is equal to-- and I'll write it in front of the x now-- 2 times x minus log base 5 of y. I'll do this in blue. Unnecessary errors can be prevented by being careful and methodical in every step. Next, utilize the Product Rule to deal with the plus symbol followed by the Quotient Rule to address the subtraction part. Example 3: Combine or condense the following log expressions into a single logarithm: Start by applying Rule 2 Power Rule in reverse to take care of the constants or numbers on the left of the logs.

This is how it looks when you solve it.

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