Write as a Single Logarithm 3 log base 4 of 2x+1-2 log base 4 of 2x-1+2

$3 \log_{4} (2 x + 1) - 2 \log_{4} (2 x - 1) + 2$

Step 1

Simplify each term.

Simplify $3 \log_{4} (2 x + 1)$ by moving $3$ inside the logarithm.

$\log_{4} ({(2 x + 1)}^{3}) - 2 \log_{4} (2 x - 1) + 2$

Simplify $- 2 \log_{4} (2 x - 1)$ by moving $2$ inside the logarithm.

$\log_{4} ({(2 x + 1)}^{3}) - \log_{4} ({(2 x - 1)}^{2}) + 2$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{4} (\frac{{(2 x + 1)}^{3}}{{(2 x - 1)}^{2}}) + 2$