Precalculus Examples

$\frac{\log (11) \log (3) \log (11)}{2 \log (16)}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $\log (11)$ to the power of $1$ .

$\frac{\log^{1} (11) \log (11) \log (3)}{2 \log (16)}$

Step 1.2

Raise $\log (11)$ to the power of $1$ .

$\frac{\log^{1} (11) \log^{1} (11) \log (3)}{2 \log (16)}$

Step 1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\log (11)}^{1 + 1} \log (3)}{2 \log (16)}$

Step 1.4

Add $1$ and $1$ .

$\frac{\log^{2} (11) \log (3)}{2 \log (16)}$

Step 2

Simplify $2 \log (16)$ by moving $2$ inside the logarithm.

$\frac{\log^{2} (11) \log (3)}{\log (16^{2})}$

Step 3

Raise $16$ to the power of $2$ .

$\frac{\log^{2} (11) \log (3)}{\log (256)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log^{2} (11) \log (3)}{\log (256)}$

Decimal Form:

$0.21486122 \dots$