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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)

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Answer:

[tex]\mathbf{1 + log_3 ( 45x + 27y)}[/tex]

Step-by-step explanation:

Given that:

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

Since [tex]log (ab) = log \ a +log \ b[/tex]

Then

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

Since [tex]log_a (a) = 1[/tex]

Then

[tex]log_3 (3) + log_3 ( 45 + 27y) = 1 + log_3 ( 45x + 27y)[/tex]

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