Precalculus Examples

$\log (5 e) + \log (6 e) + \log (e)$

Step 1

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

$\log (5 e (6 e)) + \log (e)$

Step 2

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

$\log (5 e (6 e) e)$

Step 3

Multiply $e$ by $e$ by adding the exponents.

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Step 3.1

Move $e$ .

$\log (5 (e e) \cdot 6 e)$

Step 3.2

Multiply $e$ by $e$ .

$\log (5 e^{2} \cdot 6 e)$

Step 4

Multiply $e^{2}$ by $e$ by adding the exponents.

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Step 4.1

Move $e$ .

$\log (5 (e e^{2}) \cdot 6)$

Step 4.2

Multiply $e$ by $e^{2}$ .

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Step 4.2.1

Raise $e$ to the power of $1$ .

$\log (5 (e^{1} e^{2}) \cdot 6)$

Step 4.2.2

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

$\log (5 e^{1 + 2} \cdot 6)$

Step 4.3

Add $1$ and $2$ .

$\log (5 e^{3} \cdot 6)$

Step 5

Multiply $6$ by $5$ .

$\log (30 e^{3})$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\log (30 e^{3})$

Decimal Form:

$2.78000470 \dots$