Question

Condensing Logarithmic Expression In Exercise,use the properties of logarithms to rewrite the expression as the logarithm of a single quantity.See example 4.

3/2[In x(x^2 + 1) - In(x + 1)]

Answer 1

`[ln (x(x^2 + 1))/((x + 1))]^(3)/(2)`

Explanation:

`(3)/(2) [ln x(x^2 + 1) - ln(x + 1)]`

ln(m/n)= lnm - ln(n)

`(3)/(2)[ln x(x^2 + 1) - ln(x + 1)]`

`(3)/(2)[ln (x(x^2 + 1))/((x + 1))]`

3/2 is before ln. so we move the fraction 3/2 to the exponent

as per log property we move the fraction to the exponent

`[ln (x(x^2 + 1))/((x + 1))]^(3)/(2)`