en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((ab)/(cd))

Solution

simplify

ln (\frac{ab}{c d})

Solution

ln (a) + ln (b) - ln (c) - ln (d)

Solution steps

ln (\frac{ab}{c d})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{ab}{c d}) = ln (ab) - ln (c d)

= ln (ab) - ln (c d)

Apply log rule:

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

ln (ab) = ln (a) + ln (b), ln (c d) = ln (c) + ln (d)

= ln (a) + ln (b) - (ln (c) + ln (d))

- (ln (c) + ln (d)) : - ln (c) - ln (d)

= ln (a) + ln (b) - ln (c) - ln (d)

Popular Examples

simplify 1ln(68/75)simplify

1 ln (\frac{68}{75})

simplify ln(e^2-sqrt(e^4-1))-ln(2-sqrt(5))simplify

ln (e^{2} - e^{4} - 1) - ln (2 - 5)

simplify ln((5.6)/(0.25)*10^{-7})simplify

ln (\frac{5.6}{0.25} \cdot 1 0^{- 7})

simplify 1/(2*(0.15*10^{-9))}*ln(1/(0.02))simplify

\frac{1}{2 \cdot ( 0.15 \cdot 1 0 ^{- 9} )} \cdot ln (\frac{1}{0.02})

expand log_{10}((2(7+x)^4)/(x^5))expand

lo g_{10} (\frac{2 ( 7 + x ) ^{4}}{x ^{5}})

Frequently Asked Questions (FAQ)

What is ln((ab)/(cd)) ?
The solution to ln((ab)/(cd)) is ln(a)+ln(b)-ln(c)-ln(d)