Write as a Single Logarithm log base 5 of 11+2 log base 5 of 8

$\log_{5} (11) + 2 \log_{5} (8)$

Step 1

Simplify each term.

Simplify $2 \log_{5} (8)$ by moving $2$ inside the logarithm.

$\log_{5} (11) + \log_{5} (8^{2})$

Raise $8$ to the power of $2$ .

$\log_{5} (11) + \log_{5} (64)$

Step 2

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

$\log_{5} (11 \cdot 64)$

Step 3

Multiply $11$ by $64$ .

$\log_{5} (704)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{5} (704)$

Decimal Form:

$4.07395545 \dots$