Calculus Examples

$4 \ln (2) + \ln (x) + \ln (5)$

Step 1

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

$4 \ln (2) + \ln (x \cdot 5)$

Step 2

Simplify each term.

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Step 2.1

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

$\ln (2^{4}) + \ln (x \cdot 5)$

Step 2.2

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

$\ln (16) + \ln (x \cdot 5)$

Step 2.3

Move $5$ to the left of $x$ .

$\ln (16) + \ln (5 x)$

Step 3

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

$\ln (16 (5 x))$

Step 4

Multiply $5$ by $16$ .

$\ln (80 x)$