Question

Use properties of logarithms to condense the logarithmic expression below. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 1/8 ln x + ln y 1/8 ln x + ln y = (Simplify your answer.) Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Evaluate logarithmic expressions if possible. 2 ln(x + 7) - 9 ln x 2 ln(x + 7) - 9 ln x =

Answer 1

(a)
`\ln (x^{(1)/(8)}y)`

(b)
`\ln (((x+7)^2)/(x^9))`

Explanation:

The given expression is

`(1)/(8)\ln x+\ln y`

Using the properties of logarithm we get

`\ln (x^{(1)/(8)})+\ln y`
`[\because \ln a^b=b\ln a]`

`\ln (x^{(1)/(8)}y)`
`[\because \ln(ab)=\ln a+\ln b]`

Therefore, the simplified form of given expression is
`\ln (x^{(1)/(8)}y)`.

The given expression is

`2\ln (x+7)-9\ln x`

Using the properties of logarithm we get

`\ln (x+7)^2-\ln x^9`
`[\because \ln a^b=b\ln a]`

`\ln (((x+7)^2)/(x^9))`
`[\because \ln((a)/(b))=\ln a-\ln b]`

Therefore, the simplified form of given expression is
`\ln (((x+7)^2)/(x^9))`.