en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(2)+ln(x)-ln(x-1)

Solution

simplify

ln (2) + ln (x) - ln (x - 1)

Solution

ln (\frac{2 x}{x - 1})

Solution steps

ln (2) + ln (x) - ln (x - 1)

Apply log rule:

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

ln (2) + ln (x) = ln (2 x)

= ln (2 x) - ln (x - 1)

Apply log rule:

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

ln (2 x) - ln (x - 1) = ln (\frac{2 x}{x - 1})

= ln (\frac{2 x}{x - 1})

Popular Examples

simplify log_{2}((2x+3)/8)simplify

lo g_{2} (\frac{2 x + 3}{8})

simplify log_{3}((9x^2(y+3))/(\sqrt[3]{x^2+2)})simplify

simplify 2(log_{7}(x)+3log_{7}(y)-4log_{7}(z))simplify

2 (lo g_{7} (x) + 3 lo g_{7} (y) - 4 lo g_{7} (z))

simplify log_{3}((27b^3sqrt(y^2-3))/(y(x+3)^2))simplify

lo g_{3} (\frac{27 b ^{3} y ^{2} - 3}{y ( x + 3 ) ^{2}})

simplify log_{10}(x)+3log_{10}(y)-3log_{10}(z)simplify

lo g_{10} (x) + 3 lo g_{10} (y) - 3 lo g_{10} (z)

Frequently Asked Questions (FAQ)

What is ln(2)+ln(x)-ln(x-1) ?
The solution to ln(2)+ln(x)-ln(x-1) is ln((2x)/(x-1))