Simplify/Condense 3 log base 7 of 4+ log base 7 of 6

$3 \log_{7} (4) + \log_{7} (6)$

Step 1

Simplify each term.

Simplify $3 \log_{7} (4)$ by moving $3$ inside the logarithm.

$\log_{7} (4^{3}) + \log_{7} (6)$

Raise $4$ to the power of $3$ .

$\log_{7} (64) + \log_{7} (6)$

Step 2

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

$\log_{7} (64 \cdot 6)$

Step 3

Multiply $64$ by $6$ .

$\log_{7} (384)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{7} (384)$

Decimal Form:

$3.05802534 \dots$