Simplify/Condense 2 log base b of 2- log base b of 4

$2 \log_{b} (2) - \log_{b} (4)$

Step 1

Simplify each term.

Simplify $2 \log_{b} (2)$ by moving $2$ inside the logarithm.

$\log_{b} (2^{2}) - \log_{b} (4)$

Raise $2$ to the power of $2$ .

$\log_{b} (4) - \log_{b} (4)$

Step 2

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

$\log_{b} (\frac{4}{4})$

Step 3

Divide $4$ by $4$ .

$\log_{b} (1)$

Step 4

Logarithm base $b$ of $1$ is $0$ .

$0$