Question

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator. log3(135x+81y)

Answer 1

`\mathbf{1 + log_3 ( 45x + 27y)}`

Explanation:

Given that:

`log_3 (135x + 81 y) \\ \\ = log_3 [ 3 (45x + 27y) ]`

Since
`log (ab) = log \ a +log \ b`

Then

`log_3 [ 3 (45x + 27y) ] = log_3 (3) + log_3 ( 45x + 27y)`

Since
`log_a (a) = 1`

Then

`log_3 (3) + log_3 ( 45 + 27y) = 1 + log_3 ( 45x + 27y)`