Question

Condensing Logarithmic Expressions In Exercise, use the properties of logarithm to rewrite the expression as the logarithm of a single quantity.

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

Answer 1

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

Explanation:

We have given expression
`(1)/(2)[lnx+3ln(x+1)-ln(x-2)]`

We have to simplify this expression using logarithmic property

According to logarithmic property when two or more log function are added to each other then the functions are multiplied with each other

So
`(1)/(2)[lnx+3ln(x+1)-ln(x-2)]=(1)/(2)[ln(x* (x+1)^3-ln(x-2))]`

Now again using log property

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

Now using exponent property of logarithm

`(1)/(2)[ln(x* (x+1)^3)/(x-2)]=[ln(x* (x+1)^3)/(x-2)]^{(1)/(2)}`