# What is the power property of logarithms?

## What is the power property of logarithms?

Therefore, the Power Property says that if there is an exponent within a logarithm, we can pull it out in front of the logarithm.

What is the product of logs?

Because the logarithm of a product is the sum of the logarithms of the factors, the logarithm of a number, x , to an exponent, p , is the same as the logarithm of x added together p times, so it is equal to plogb(x).

### What is the property of equality for logarithmic equations?

The equality rule says that if you have two logarithms with the same base that are equivalent, then what is inside the logarithms are equivalent to each other.

What is logarithmic inequality?

Logarithmic inequalities are inequalities in which one (or both) sides involve a logarithm. Like exponential inequalities, they are useful in analyzing situations involving repeated multiplication, such as in the cases of interest and exponential decay.

#### What is log of a product?

The log of a product is equal to the sum of the logs of its factors. There are a few rules that can be used when solving logarithmic equations. One of these rules is the logarithmic product rule, which can be used to separate complex logs into multiple terms.

What are the properties of natural log?

Properties of the Natural Logarithm The domain of the natural logarithm is the set of all positive real numbers. (You can’t take the log of a negative number!) The image of the natural logarithm is the set of all real numbers. The natural logarithm is differentiable.

## What are the properties of logs?

Logs have four basic properties: Product Rule: The log of a product is equal to the sum of the log of the first base and the log of the second base (). Quotient Rule : The log of a quotient is equal to the difference of the logs of the numerator and denominator (). Power Rule : The log of a power is equal to the power times the log of the base ().

What is log power rule?

Power Rule: The log of a power is equal to the power times the log of the base (). Change of Base Formula: The log of a new base is the log of the new base divided by the log of the old base in the new base ().