Precalculus Examples

$\log_{6} (\frac{1}{36}) + \log_{6} (6^{2}) + 5^{\log_{6} (1)}$

Step 1

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

$\log_{6} (\frac{1}{36} \cdot 6^{2}) + 5^{\log_{6} (1)}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Raise $6$ to the power of $2$ .

$\log_{6} (\frac{1}{36} \cdot 36) + 5^{\log_{6} (1)}$

Step 2.2

Cancel the common factor of $36$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

$\log_{6} (\frac{1}{36} \cdot 36) + 5^{\log_{6} (1)}$

Step 2.2.2

Rewrite the expression.

$\log_{6} (1) + 5^{\log_{6} (1)}$

Step 2.3

Logarithm base $6$ of $1$ is $0$ .

$0 + 5^{\log_{6} (1)}$

Step 2.4

Logarithm base $6$ of $1$ is $0$ .

$0 + 5^{0}$

Step 2.5

Anything raised to $0$ is $1$ .

$0 + 1$

Step 3

Add $0$ and $1$ .

$1$