Question

What is 4log 1/2w+(2log 1/2u-3log 1/2v) written as a single logarithm

Answer 1

B. on edge = log1/2 w^4(u^2/v^3)

I gotchu bois

Answer 2

The given expression is

`4log_(1/2)w+(2 log_(1/2)u-3log_(1/2)v)`

First we use the following rule

`a \ log_(b) c = log _(b) c^a`

And on using this rule, we will get

`log_(1/2) w^4 + ( log_(1/2)u^2-log_(1/2)v^3 )`

Now we use the following two rules

`log a + log b = log(ab) \\ log a- log b =log( (a)/(b) )`

And on using these two rules, we will get

`=log_(1/2)w^4 + log_(1/2) ( (u^2)/(v^3)) \\ = log_(1/2) (( w^4 u^2)/(v^3) )`