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

2 Answers
Rachel
Jun 25, 2017

#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)#

Jim G.
Jun 25, 2017

#4log_8x#

Explanation:

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

#• logx^nhArrnlogx#

#rArrlog_8x^4=4log_8x#

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