# What are 2/3 properties of logarithms examples and their property and what is the significance of using those properties?

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Expert Answers

crmhaske | Certified Educator

Using the properties of logarithms makes solving for logarithmic expressions possible, hence their importance.

The most important property of a logarithm:

`log_ax=b-gta^b=x`

Some other properties of logarithms:

`log_a(xy)=log_a(x)+log_a(y)`

`log_a(x/y)=log_a(x)-log_a(y)`

`log_ax^n=nlog_ax`

`log_aroot(n)x=(log_ax)/n`

To illustrate with an example:

`262144=4^x`

`log262144=log4^x`

`log262144=xlog4`

`x=log262144/log4`

`x=9`

Further Reading: