Algebra Examples

$\log_{2} (288) - \frac{1}{2} \cdot \log_{2} (81)$

Step 1

Simplify each term.

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Step 1.1

Multiply $- \frac{1}{2} \log_{2} (81)$ .

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Step 1.1.1

Reorder $\log_{2} (81)$ and $\frac{1}{2}$ .

$\log_{2} (288) - (\frac{1}{2} \log_{2} (81))$

Step 1.1.2

Simplify $\frac{1}{2} \log_{2} (81)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{2} (288) - \log_{2} (81^{\frac{1}{2}})$

Step 1.2

Rewrite $81$ as $9^{2}$ .

$\log_{2} (288) - \log_{2} ({(9^{2})}^{\frac{1}{2}})$

Step 1.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{2} (288) - \log_{2} (9^{2 (\frac{1}{2})})$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

$\log_{2} (288) - \log_{2} (9^{2 (\frac{1}{2})})$

Step 1.4.2

Rewrite the expression.

$\log_{2} (288) - \log_{2} (9^{1})$

Step 1.5

Evaluate the exponent.

$\log_{2} (288) - \log_{2} (9)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{2} (\frac{288}{9})$

Step 3

Logarithm base $2$ of $\frac{288}{9}$ is $5$ .

$5$