Algebra Examples

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

Step 1

Expand $\log_{2} ({(\frac{5}{4})}^{x - 3})$ by moving $x - 3$ outside the logarithm.

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

Step 2

Rewrite $\log_{2} (\frac{5}{4})$ as $\log_{2} (5) - \log_{2} (4)$ .

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

Step 3

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

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

Step 4

Multiply $- 1$ by $2$ .

$(x - 3) (\log_{2} (5) - 2)$

Step 5

Expand $(x - 3) (\log_{2} (5) - 2)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$x (\log_{2} (5) - 2) - 3 (\log_{2} (5) - 2)$

Step 5.2

Apply the distributive property.

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

Step 5.3

Apply the distributive property.

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

Step 6

Simplify each term.

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Step 6.1

Move $- 2$ to the left of $x$ .

$x \log_{2} (5) - 2 \cdot x - 3 \log_{2} (5) - 3 \cdot - 2$

Step 6.2

Multiply $- 3$ by $- 2$ .

$x \log_{2} (5) - 2 x - 3 \log_{2} (5) + 6$