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Rewrite the logarithmic expression as the sum and difference of logarithms. If exponents may be written as the coefficient of a logarithm, write exponents as the coefficient. G(y)

Respuesta :

MrRoyal

Answer:

[tex]G(y) = 4\ln(2y+1) - \frac{1}{2}\ln(y^2 + 1)[/tex]

Step-by-step explanation:

Given

[tex]G(y) = \ln(\frac{(2y+1)^4}{\sqrt{y^2 + 1}})[/tex]

Required

Rewrite as sum and difference

Apply laws of logarithm:

[tex]G(y) = \ln(2y+1)^4 - \ln({\sqrt{y^2 + 1})[/tex]

Rewrite the exponents

[tex]G(y) = \ln(2y+1)^4 - \ln(y^2 + 1)^\frac{1}{2}[/tex]

Convert exponents to coefficients

[tex]G(y) = 4\ln(2y+1) - \frac{1}{2}\ln(y^2 + 1)[/tex]

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