Algebra Examples

$\log_{4} (\log_{4} (2 x)) = 1$

Rewrite $\log_{4} (\log_{4} (2 x)) = 1$ 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 $b^{y} = x$ .

$4^{1} = \log_{4} (2 x)$

Solve for $x$ .

Tap for more steps...

Rewrite the equation as $\log_{4} (2 x) = 4^{1}$ .

$\log_{4} (2 x) = 4$

Rewrite $\log_{4} (2 x) = 4^{1}$ 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 $b^{y} = x$ .

$4^{4^{1}} = 2 x$

Solve for $x$ .

Tap for more steps...

Rewrite the equation as $2 x = 4^{4^{1}}$ .

$2 x = 4^{4^{1}}$

Divide each term in $2 x = 4^{4^{1}}$ by $2$ and simplify.

Tap for more steps...

Divide each term in $2 x = 4^{4^{1}}$ by $2$ .

$\frac{2 x}{2} = \frac{4^{4^{1}}}{2}$

Simplify the left side.

Tap for more steps...

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2 x}{2} = \frac{4^{4^{1}}}{2}$

Divide $x$ by $1$ .

$x = \frac{4^{4^{1}}}{2}$

Simplify the right side.

Tap for more steps...

Simplify the numerator.

Tap for more steps...

Evaluate the exponent.

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

Raise $4$ to the power of $4$ .

$x = \frac{256}{2}$

Divide $256$ by $2$ .

$x = 128$