Finite Math Examples

$\log (5 \log_{2} (x)) = 1$

Step 1

Rewrite $\log (5 \log_{2} (x)) = 1$ 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 $b^{y} = x$ .

$10^{1} = 5 \log_{2} (x)$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $5 \log_{2} (x) = 10^{1}$ .

$5 \log_{2} (x) = 10$

Step 2.2

Divide each term in $5 \log_{2} (x) = 10^{1}$ by $5$ and simplify.

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Step 2.2.1

Divide each term in $5 \log_{2} (x) = 10^{1}$ by $5$ .

$\frac{5 \log_{2} (x)}{5} = \frac{10^{1}}{5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{5 \log_{2} (x)}{5} = \frac{10^{1}}{5}$

Step 2.2.2.1.2

Divide $\log_{2} (x)$ by $1$ .

$\log_{2} (x) = \frac{10^{1}}{5}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Evaluate the exponent.

$\log_{2} (x) = \frac{10}{5}$

Step 2.2.3.2

Divide $10$ by $5$ .

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

Step 2.3

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

$2^{2} = x$

Step 2.4

Solve for $x$ .

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Step 2.4.1

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

$x = 2^{2}$

Step 2.4.2

Raise $2$ to the power of $2$ .

$x = 4$