Simplify/Condense 5 log of x+ log of 20- log of 10

$5 \log (x) + \log (20) - \log (10)$

Step 1

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

$5 \log (x) + \log (\frac{20}{10})$

Step 2

Simplify each term.

Simplify $5 \log (x)$ by moving $5$ inside the logarithm.

$\log (x^{5}) + \log (\frac{20}{10})$

Divide $20$ by $10$ .

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

Step 3

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

$\log (x^{5} \cdot 2)$

Step 4

Move $2$ to the left of $x^{5}$ .

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