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.

2[ In x + 1/4In(x + 1)]

Answer 1

`(lnx(x + 1)^{(1)/(4)})^2`

Explanation:

`2[ln x +(1)/(4)ln(x + 1)]`

m ln(n)= ln(n)^m

we move the term before ln to the exponent

`2[ln x +ln(x + 1)^{(1)/(4)}]`

`ln m +ln n = ln(mn)`

`2[ln x +ln(x + 1)^{(1)/(4)}]`

`2[ln(x(x + 1)^{(1)/(4)})]`

as per log property , move 2 to the exponent

`(lnx(x + 1)^{(1)/(4)})^2`