Finite Math Examples

$3 \log (4) + 5 \log (2) = x$

Step 1

Rewrite the equation as $x = 3 \log (4) + 5 \log (2)$ .

$x = 3 \log (4) + 5 \log (2)$

Step 2

Simplify $3 \log (4) + 5 \log (2)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$x = \log (4^{3}) + 5 \log (2)$

Step 2.1.2

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

$x = \log (64) + 5 \log (2)$

Step 2.1.3

Simplify $5 \log (2)$ by moving $5$ inside the logarithm.

$x = \log (64) + \log (2^{5})$

Step 2.1.4

Raise $2$ to the power of $5$ .

$x = \log (64) + \log (32)$

Step 2.2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$x = \log (64 \cdot 32)$

Step 2.3

Multiply $64$ by $32$ .

$x = \log (2048)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \log (2048)$

Decimal Form:

$x = 3.31132995 \dots$