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

Answer:

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

Step-by-step 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

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