Precalculus Examples

$(2 \log (4)) - (\log (3)) + 2 \log (43.3012 - 4)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (4)$ by moving $2$ inside the logarithm.

$\log (4^{2}) - (\log (3)) + 2 \log (43.3012 - 4)$

Step 1.2

Raise $4$ to the power of $2$ .

$\log (16) - (\log (3)) + 2 \log (43.3012 - 4)$

Step 1.3

Subtract $4$ from $43.3012$ .

$\log (16) - \log (3) + 2 \log (39.3012)$

Step 1.4

Log base $10$ of $39.3012$ is approximately $1.59440581$ .

$\log (16) - \log (3) + 2 \cdot 1.59440581$

Step 1.5

Multiply $2$ by $1.59440581$ .

$\log (16) - \log (3) + 3.18881162$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{16}{3}) + 3.18881162$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{16}{3}) + 3.18881162$

Decimal Form:

$3.91581035 \dots$