Algebra Examples

$- \frac{5}{2} \log_{2} (4) - 4 \log_{2} (x) + \frac{3}{2} \log_{2} (y)$

Step 1

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

$- \frac{5}{2} \cdot 2 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} \cdot 2 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Step 2.2

Cancel the common factor.

$\frac{- 5}{2} \cdot 2 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Step 2.3

Rewrite the expression.

$- 5 - 4 \log_{2} (x) + \frac{3}{2} \cdot \log_{2} (y)$

Step 3

Simplify $- 4 \log_{2} (x)$ by moving $4$ inside the logarithm.

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

Step 4

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

$- 5 - \log_{2} (x^{4}) + \log_{2} (y^{\frac{3}{2}})$