Algebra Examples

$7 \ln (x) + 2 \ln (3) - 5 \ln (y)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (x^{7}) + 2 \ln (3) - 5 \ln (y)$

Step 1.2

Simplify $2 \ln (3)$ by moving $2$ inside the logarithm.

$\ln (x^{7}) + \ln (3^{2}) - 5 \ln (y)$

Step 1.3

Raise $3$ to the power of $2$ .

$\ln (x^{7}) + \ln (9) - 5 \ln (y)$

Step 1.4

Simplify $- 5 \ln (y)$ by moving $5$ inside the logarithm.

$\ln (x^{7}) + \ln (9) - \ln (y^{5})$

Step 2

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

$\ln (x^{7} \cdot 9) - \ln (y^{5})$

Step 3

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

$\ln (\frac{x^{7} \cdot 9}{y^{5}})$

Step 4

Move $9$ to the left of $x^{7}$ .

$\ln (\frac{9 x^{7}}{y^{5}})$