Question

How do you use the properties of logarithms to expand `log_8 (x^4)`?

Answer 1

`4log_8(x)`

Explanation:

To expand this logarithm, the first thing we can do is change the `x^4`:

`log_8(x^4)`

The argument is, which in this case is `x^4`, can be rewritten. We can move the "power of four" to the front of the expression, using the third property of logarithims, which states `log_a u^color(red)(n) = color(red)(n) log_a u`

Using that property, we get

`4log_8(x)`

Answer 2

`4log_8x`

Explanation:

`"using the "color(blue)"law of logarithms"`

`• logx^nhArrnlogx`

`rArrlog_8x^4=4log_8x`