Calculus Examples

$2 \ln (7) - \ln (x) - \ln (2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \ln (7)$ by moving $2$ inside the logarithm.

$\ln (7^{2}) - \ln (x) - \ln (2)$

Step 1.2

Raise $7$ to the power of $2$ .

$\ln (49) - \ln (x) - \ln (2)$

Step 2

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

$\ln (\frac{49}{x}) - \ln (2)$

Step 3

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

$\ln (\frac{\frac{49}{x}}{2})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\ln (\frac{49}{x} \cdot \frac{1}{2})$

Step 5

Multiply $\frac{49}{x}$ by $\frac{1}{2}$ .

$\ln (\frac{49}{x \cdot 2})$

Step 6

Move $2$ to the left of $x$ .

$\ln (\frac{49}{2 x})$