Precalculus Examples

$\log (5) (x + 1) + \log (x) + \log (5) \cdot 20$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\log (5) x + \log (5) \cdot 1 + \log (x) + \log (5) \cdot 20$

Step 1.2

Multiply $\log (5)$ by $1$ .

$\log (5) x + \log (5) + \log (x) + \log (5) \cdot 20$

Step 1.3

Multiply $\log (5) \cdot 20$ .

Tap for more steps...

Step 1.3.1

Reorder $\log (5)$ and $20$ .

$\log (5) x + \log (5) + \log (x) + 20 \cdot \log (5)$

Step 1.3.2

Simplify $20 \cdot \log (5)$ by moving $20$ inside the logarithm.

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

Step 1.4

Raise $5$ to the power of $20$ .

$\log (5) x + \log (5) + \log (x) + \log (95367431640625)$

Step 2

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

$\log (5) x + \log (5 x) + \log (95367431640625)$

Step 3

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

$\log (5) x + \log (5 x \cdot 95367431640625)$

Step 4

Multiply $95367431640625$ by $5$ .

$\log (5) x + \log (476837158203125 x)$

Step 5

Reorder factors in $\log (5) x + \log (476837158203125 x)$ .

$x \log (5) + \log (476837158203125 x)$