Algebra Examples

$\log_{x} (5) + \log_{x} (12) = 7$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

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

$\log_{x} (5 \cdot 12) = 7$

Step 1.2

Multiply $5$ by $12$ .

$\log_{x} (60) = 7$

Step 2

Rewrite $\log_{x} (60) = 7$ 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 $b^{y} = x$ .

$x^{7} = 60$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[7]{60}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[7]{60}$

Decimal Form:

$x = 1.79482292 \dots$