Algebra Examples

$\log (3 x) - \log (10)$

Step 1

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

$\log (\frac{3 x}{10})$

Step 2

Rewrite $\frac{3 x}{10}$ as $3 x \cdot 10^{- 1}$ .

$\log (3 x \cdot 10^{- 1})$

Step 3

Rewrite $\log (3 x \cdot 10^{- 1})$ as $\log (3 x) + \log (10^{- 1})$ .

$\log (3 x) + \log (10^{- 1})$

Step 4

Use logarithm rules to move $- 1$ out of the exponent.

$\log (3 x) - \log (10)$

Step 5

Logarithm base $10$ of $10$ is $1$ .

$\log (3 x) - 1 \cdot 1$

Step 6

Multiply $- 1$ by $1$ .

$\log (3 x) - 1$