Algebra Examples

$3 \log (2 x) = 4$

Step 1

Divide each term in $3 \log (2 x) = 4$ by $3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $3 \log (2 x) = 4$ by $3$ .

$\frac{3 \log (2 x)}{3} = \frac{4}{3}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{3 \log (2 x)}{3} = \frac{4}{3}$

Step 1.2.1.2

Divide $\log (2 x)$ by $1$ .

$\log (2 x) = \frac{4}{3}$

Step 2

Rewrite $\log (2 x) = \frac{4}{3}$ 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 $b^{y} = x$ .

$10^{\frac{4}{3}} = 2 x$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Rewrite the equation as $2 x = 10^{\frac{4}{3}}$ .

$2 x = 10^{\frac{4}{3}}$

Step 3.2

Divide each term in $2 x = 10^{\frac{4}{3}}$ by $2$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $2 x = 10^{\frac{4}{3}}$ by $2$ .

$\frac{2 x}{2} = \frac{10^{\frac{4}{3}}}{2}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{10^{\frac{4}{3}}}{2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10^{\frac{4}{3}}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10^{\frac{4}{3}}}{2}$

Decimal Form:

$x = 10.77217345 \dots$