# How can you use the properties of logarithms to condense logarithmic expressions?

**Condense logarithmic expressions**

- Apply the power
**property**first. Identify terms that are products of factors and a**logarithm**, and rewrite each as the**logarithm**of a power. - Next apply the product
**property**. Rewrite sums of**logarithms**as the**logarithm**of a product. - Apply the quotient
**property**last.

Hereof, what does it mean to condense a logarithmic expression?

When they tell you to "simplify" a **log expression**, this usually **means** they will have given you lots of **log** terms, each containing a simple argument, and they want you to combine everything into one **log** with a complicated argument. "Simplifying" in this context usually **means** the opposite of "expanding".

**equal to**2.718281828459. The natural logarithm of x is generally written as

**ln**x, log

_{e}x, or sometimes, if the base e is implicit, simply log x.

One may also ask, how do you do properties of logarithms?

The **logarithm** of a product **property** says log_{2} 8a = log_{2} 8 + log_{2} a, and log_{2} 8 = 3. You can use the similarity between the **properties** of exponents and **logarithms** to find the **property** for the **logarithm** of a quotient. With exponents, to multiply two numbers with the same base, you add the exponents.

The **laws** apply to **logarithms** of any base but the same base must be used throughout a calculation. This **law** tells us how to add two **logarithms** together. Adding log A and log B results in the **logarithm** of the product of A and B, that is log AB. The same base, in this case 10, is used throughout the calculation.