Question

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)

Answer 1

Answer:

$G(y) = 4\ln(2y+1) - \frac{1}{2}\ln(y^2 + 1)$

Step-by-step explanation:

Given

$G(y) = \ln(\frac{(2y+1)^4}{\sqrt{y^2 + 1}})$

Required

Rewrite as sum and difference

Apply laws of logarithm:

$G(y) = \ln(2y+1)^4 - \ln({\sqrt{y^2 + 1})$

Rewrite the exponents

$G(y) = \ln(2y+1)^4 - \ln(y^2 + 1)^\frac{1}{2}$

Convert exponents to coefficients

$G(y) = 4\ln(2y+1) - \frac{1}{2}\ln(y^2 + 1)$