29.4k views
3 votes
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)

1 Answer

5 votes

Answer:


G(y) = 4\ln(2y+1) - (1)/(2)\ln(y^2 + 1)

Explanation:

Given


G(y) = \ln(((2y+1)^4)/(√(y^2 + 1)))

Required

Rewrite as sum and difference

Apply laws of logarithm:


G(y) = \ln(2y+1)^4 - \ln({√(y^2 + 1))

Rewrite the exponents


G(y) = \ln(2y+1)^4 - \ln(y^2 + 1)^(1)/(2)

Convert exponents to coefficients


G(y) = 4\ln(2y+1) - (1)/(2)\ln(y^2 + 1)

User Soni Kumar
by
7.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.