Algebra Examples

$\log_{2} (9 x) - \log_{2} (9) = 1$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

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

$\log_{2} (\frac{9 x}{9}) = 1$

Step 1.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$\log_{2} (\frac{9 x}{9}) = 1$

Step 1.2.2

Divide $x$ by $1$ .

$\log_{2} (x) = 1$

Step 2

Rewrite $\log_{2} (x) = 1$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$2^{1} = x$

Step 3

Rewrite the equation as $x = 2^{1}$ .

$x = 2$