# Rewrite as a sum or difference of multiple logarithms explained

Other textbooks refer to this as simplifying logarithms.

I'll do this in blue. So we can use some logarithm properties.

### Properties of logarithms examples

Rule 6: Log of Exponent Rule The logarithm of an exponential number where its base is the same as the base of the log equals the exponent. Log base 5 of 25 to the x over y using this property means that it's the same thing as log base 5 of 25 to the x power minus log base 5 of y. Description of Each Logarithm Rule Rule1: Product Rule The logarithm of the product of numbers is the sum of logarithms of individual numbers. Unnecessary errors can be prevented by being careful and methodical in every step. Rule 7: Exponent of Log Rule Raising the logarithm of a number by its base equals the number. 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. It seems like the relevant logarithm property here is if I have log base x of a to the b power, that's the same thing as b times log base x of a, that this exponent over here can be moved out front, which is what we did it right over there. The square root can definitely simplify the perfect square 81 and the y12 because it has an even power. Next, utilize the Product Rule to deal with the plus symbol followed by the Quotient Rule to address the subtraction part. I'll do this in blue. Just a reminder, you add the exponents during multiplication and subtract during division.

Example 2: Combine or condense the following log expressions into a single logarithm: The difference between logarithmic expressions implies the Quotient Rule. Remember that Power Rule brings down the exponent, so the opposite direction is to put it up.

## Logarithm calculator

And we're done. Example 2: Combine or condense the following log expressions into a single logarithm: The difference between logarithmic expressions implies the Quotient Rule. So we can use some logarithm properties. And then, of course, we have minus log base 5 of y. Properties of logarithms Video transcript We're asked to simplify log base 5 of 25 to the x power over y. Example 4: Combine or condense the following log expressions into a single logarithm: I can apply the reverse of Power rule to place the exponents on variable x for the two expressions and leave the third one for now because it is already fine. But, they all mean the same. Rule 2: Quotient Rule The logarithm of the quotient of numbers is the difference of the logarithm of individual numbers. In this problem, watch out for the opportunity where you will multiply and divide exponential expressions. Rule 6: Log of Exponent Rule The logarithm of an exponential number where its base is the same as the base of the log equals the exponent. 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.

So this simplifies to 2. This is an interesting problem because of the constant 3. Rule 7: Exponent of Log Rule Raising the logarithm of a number by its base equals the number.

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 this part right over here can be rewritten as x times the logarithm base 5 of

## Log properties list

In this problem, watch out for the opportunity where you will multiply and divide exponential expressions. It seems like the relevant logarithm property here is if I have log base x of a to the b power, that's the same thing as b times log base x of a, that this exponent over here can be moved out front, which is what we did it right over there. Remember that Power Rule brings down the exponent, so the opposite direction is to put it up. So we can use some logarithm properties. 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. Example 2: Combine or condense the following log expressions into a single logarithm: The difference between logarithmic expressions implies the Quotient Rule. I can put together that variable x and constant 2 inside a single parenthesis using division operation. I'll do this in blue. Other textbooks refer to this as simplifying logarithms. The square root can definitely simplify the perfect square 81 and the y12 because it has an even power.

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