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

`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)`