Precalculus Examples

$\log_{3} (9) + 2 \log_{2} (4) - 10^{3 \log (4)}$

Step 1

Simplify each term.

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Step 1.1

Logarithm base $3$ of $9$ is $2$ .

$2 + 2 \log_{2} (4) - 10^{3 \log (4)}$

Step 1.2

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

$2 + 2 \cdot 2 - 10^{3 \log (4)}$

Step 1.3

Multiply $2$ by $2$ .

$2 + 4 - 10^{3 \log (4)}$

Step 1.4

Simplify $3 \log (4)$ by moving $3$ inside the logarithm.

$2 + 4 - 10^{\log (4^{3})}$

Step 1.5

Exponentiation and log are inverse functions.

$2 + 4 - 4^{3}$

Step 1.6

Raise $4$ to the power of $3$ .

$2 + 4 - 1 \cdot 64$

Step 1.7

Multiply $- 1$ by $64$ .

$2 + 4 - 64$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $2$ and $4$ .

$6 - 64$

Step 2.2

Subtract $64$ from $6$ .

$- 58$