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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 =

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Answer:

(a) [tex]\ln (x^{\frac{1}{8}}y)[/tex]

(b) [tex]\ln (\dfrac{(x+7)^2}{x^9})[/tex]

Step-by-step explanation:

The given expression is

[tex]\frac{1}{8}\ln x+\ln y[/tex]

Using the properties of logarithm we get

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

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

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

The given expression is

[tex]2\ln (x+7)-9\ln x[/tex]

Using the properties of logarithm we get

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

[tex]\ln (\dfrac{(x+7)^2}{x^9})[/tex]       [tex][\because \ln(\frac{a}{b})=\ln a-\ln b][/tex]

Therefore, the simplified form of given expression is [tex]\ln (\dfrac{(x+7)^2}{x^9})[/tex].

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