Question

Fill in the missing values to make the equation true.

Answer 1

see explanation

Explanation:

using the rules of logarithms

• loga + logb = log(ab)

• loga - logb = log (
`(a)/(b)` )

• log
`x^(n)` = nlogx

(a)

`log_(4)` 5 +
`log_(4)` 3 =
`log_(4)` (5 × 3) =
`log_(4)` 15

(b)

`log_(3)` 4 -
`log_(3)` ? =
`log_(3)` (
`(4)/(7)` ) ← with a = 4 and b = 7 , then

`log_(3)` 4 -
`log_(3)` 7 =
`log_(3)`
`(4)/(7)`

(c)

`log_(5)` 81 = 4
`log_(5)` ?

note that 81 =
`3^(4)` , then

`log_(5)` 81 =
`log_(5)`
`3^(4)` = 4
`log_(5)` 3