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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 calculatorlog5 (15x + 20y)

Respuesta :

The given expression is

[tex]\log _5(15x+20y)[/tex]

Factor out the greatest common factor between 15x and 20y.

[tex]\log _5(5(3x+4y))[/tex]

Then, use the product property to expand the logarithm.

[tex]\log _55+\log _5(3x+4y)[/tex]

At last, simplify the first logarithm because its base is equal to its argument.

[tex]1+\log _5(3x+4y)[/tex]

Therefore, the simplest form of the logarithm is

[tex]1+\log _5(3x+4y)[/tex]

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