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.

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

Answer 1

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

Explanation:

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

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

m ln(x)= lnx^m

move the term before ln to the exponent

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

ln m + ln n= ln(mn)

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

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

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

Now move fraction 1/3 to the exponent

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