Precalculus Examples

$\log (5 e) + \log (e) + \log (e^{5})$

Step 1

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

$\log (5 e e) + \log (e^{5})$

Step 2

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

$\log (5 e e e^{5})$

Step 3

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

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Step 3.1

Move $e$ .

$\log (5 (e e) e^{5})$

Step 3.2

Multiply $e$ by $e$ .

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

Step 4

Multiply $e^{2}$ by $e^{5}$ by adding the exponents.

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Step 4.1

Move $e^{5}$ .

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

Step 4.2

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

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

Step 4.3

Add $5$ and $2$ .

$\log (5 e^{7})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log (5 e^{7})$

Decimal Form:

$3.73903137 \dots$