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

Answer:

(a) $\ln (x^{\frac{1}{8}}y)$

(b) $\ln (\dfrac{(x+7)^2}{x^9})$

Step-by-step explanation:

The given expression is

$\frac{1}{8}\ln x+\ln y$

Using the properties of logarithm we get

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

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

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

The given expression is

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

Using the properties of logarithm we get

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

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

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