Question

Which expression is equivalent to log 5(x/4) ^2

2log5 +log5 4
2log5 +log5 16
2log5x-2log5 4
2log5x-log5 4

Answer 1

C, is your answer.
have a blessed day

Answer 2

C) 2log5 x-2log5 4

Explanation:

The given expression is log 5(x/4) ^2

Here we have to use a set of log rules and simplify this.

i) Power rule: log
`(a)^(b)` =
`b.log(a)`

Using the power rule, we can write the given expression as

2(log 5
`((x)/(4) )`

[Here base is 5]

ii) Quotient rule: log(
`(x)/(y) ) = log x - log y`

Using the above rule, we can write as follow

2(
`log(5)x - log(5) 4`

Now we have to use the distributive property a(b + c) = ab + ac

Using the distributive property, we get

2log(5) x - 2log(5) 4 [here the base is 5.]