Algebra Examples

$\frac{2}{3} \cdot \log_{2} (27) + \frac{5}{2} \cdot \log_{2} (4)$

Step 1

Simplify $\frac{2}{3} \log_{2} (27)$ by moving $\frac{2}{3}$ inside the logarithm.

$\log_{2} (27^{\frac{2}{3}}) + \frac{5}{2} \cdot \log_{2} (4)$

Step 2

Rewrite $27$ as $3^{3}$ .

$\log_{2} ({(3^{3})}^{\frac{2}{3}}) + \frac{5}{2} \cdot \log_{2} (4)$

Step 3

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

$\log_{2} (3^{3 (\frac{2}{3})}) + \frac{5}{2} \cdot \log_{2} (4)$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$\log_{2} (3^{3 (\frac{2}{3})}) + \frac{5}{2} \cdot \log_{2} (4)$

Step 4.2

Rewrite the expression.

$\log_{2} (3^{2}) + \frac{5}{2} \cdot \log_{2} (4)$

Step 5

Raise $3$ to the power of $2$ .

$\log_{2} (9) + \frac{5}{2} \cdot \log_{2} (4)$

Step 6

Logarithm base $2$ of $4$ is $2$ .

$\log_{2} (9) + \frac{5}{2} \cdot 2$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Cancel the common factor.

$\log_{2} (9) + \frac{5}{2} \cdot 2$

Step 7.2

Rewrite the expression.

$\log_{2} (9) + 5$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\log_{2} (9) + 5$

Decimal Form:

$8.16992500 \dots$