Write as a Single Logarithm (3 log of 2)/( log of 4+ log of 3)

$\frac{3 \log (2)}{\log (4) + \log (3)}$

Step 1

Simplify $3 \log (2)$ by moving $3$ inside the logarithm.

$\frac{\log (2^{3})}{\log (4) + \log (3)}$

Step 2

Simplify the denominator.

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\log (2^{3})}{\log (4 \cdot 3)}$

Multiply $4$ by $3$ .

$\frac{\log (2^{3})}{\log (12)}$

Step 3

Raise $2$ to the power of $3$ .

$\frac{\log (8)}{\log (12)}$

Step 4

Use the change of base rule $\frac{\log_{b} (x)}{\log_{b} (a)} = \log_{a} (x)$ .

$\log_{12} (8)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{12} (8)$

Decimal Form:

$0.83682883 \dots$