en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(f(x)*g(x))

Solution

simplify

ln (f (x) \cdot g (x))

Solution

2 ln (x) + ln (f) + ln (g)

Solution steps

ln (f (x) g (x))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (f (x) g (x)) = ln (f) + ln (x) + ln (g) + ln (x)

= ln (f) + ln (x) + ln (g) + ln (x)

Simplify

ln (f) + ln (x) + ln (g) + ln (x) : 2 ln (x) + ln (f) + ln (g)

= 2 ln (x) + ln (f) + ln (g)

Popular Examples

expand log_{10}(xy)expand

lo g_{10} (x y)

simplify 14x+ln(14x)simplify

14 x + ln (14 x)

simplify 1/3 (ln(13)-ln(5))simplify

\frac{1}{3} (ln (13) - ln (5))

simplify ln((2*3)/(3*3))simplify

ln (\frac{2 \cdot 3}{3 \cdot 3})

simplify-log_{10}(2.1*10^{-7})simplify

- lo g_{10} (2.1 \cdot 1 0^{- 7})

Frequently Asked Questions (FAQ)

What is ln(f(x)*g(x)) ?
The solution to ln(f(x)*g(x)) is 2ln(x)+ln(f)+ln(g)