Algebra Examples

$\log_{2} (d) = 5 \log_{2} (2) - \log_{2} (8)$

Step 1

Simplify the right side.

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Step 1.1

Simplify $5 \log_{2} (2) - \log_{2} (8)$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Logarithm base $2$ of $2$ is $1$ .

$\log_{2} (d) = 5 \cdot 1 - \log_{2} (8)$

Step 1.1.1.2

Multiply $5$ by $1$ .

$\log_{2} (d) = 5 - \log_{2} (8)$

Step 1.1.1.3

Logarithm base $2$ of $8$ is $3$ .

$\log_{2} (d) = 5 - 1 \cdot 3$

Step 1.1.1.4

Multiply $- 1$ by $3$ .

$\log_{2} (d) = 5 - 3$

Step 1.1.2

Subtract $3$ from $5$ .

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

Step 2

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

$2^{2} = d$

Step 3

Solve for $d$ .

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Step 3.1

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

$d = 2^{2}$

Step 3.2

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

$d = 4$