Question

Rewrite the expression as a single logarithm.

Answer 1

Use main logarithm properties:

$\log_ab^k=k\log_ab;\\ \\\log_ab+\log_ac=\log_abc;\\ \\\log_ab-\log_ac=\log_a\dfrac{b}{c}.$

Then

1.

$\dfrac{1}{4}\ln x=\ln x^{\frac{1}{4}}.$

2.

$\dfrac{3}{10}\ln (x+2)=\ln (x+2)^{\frac{3}{10}}.$

3.

$\ln (x-2)-\dfrac{3}{10}\ln (x+2)=\ln \dfrac{x-2}{(x+2)^{\frac{3}{10}}}.$

4.

$5\left(\ln (x-2)-\dfrac{3}{10}\ln (x+2)\right)=5\ln \dfrac{x-2}{(x+2)^{\frac{3}{10}}}=\ln \dfrac{(x-2)^2}{(x+2)^{\frac{3}{2}}}.$

5.

$\dfrac{1}{4}\ln x+5\left(\ln (x-2)-\dfrac{3}{10}\ln (x+2)\right)=\ln x^{\frac{1}{4}}+\ln \dfrac{(x-2)^2}{(x+2)^{\frac{3}{2}}}=\ln \dfrac{x^{\frac{1}{4}}(x-2)^5}{(x+2)^{\frac{3}{2}}}=\\ \\=\ln \dfrac{\sqrt[4]{x}(x-2)^5}{\sqrt{(x+2)^3}}.$

Answer: correct choice is B

Answer 2

Answer:

Answer is B

Step-by-step explanation: