What is ln(x/(x-10))+ln((x+10)/x)-ln(x^2-100) ?

The solution to ln(x/(x-10))+ln((x+10)/x)-ln(x^2-100) is -ln((x-10)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x/(x-10))+ln((x+10)/x)-ln(x^2-100)

simplify

ln (\frac{x}{x - 10}) + ln (\frac{x + 10}{x}) - ln (x^{2} - 100)

- ln ((x - 10)^{2})

Solution steps

ln (\frac{x}{x - 10}) + ln (\frac{x + 10}{x}) - ln (x^{2} - 100)

Apply log rule:

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

ln (\frac{x}{x - 10}) + ln (\frac{x + 10}{x}) = ln (\frac{x}{x - 10} \cdot \frac{x + 10}{x})

= ln (\frac{x}{x - 10} \cdot \frac{x + 10}{x}) - ln (x^{2} - 100)

Simplify

\frac{x}{x - 10} \cdot \frac{x + 10}{x} : \frac{x + 10}{x - 10}

= ln (\frac{x + 10}{x - 10}) - ln (x^{2} - 100)

Apply log rule:

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

ln (\frac{x + 10}{x - 10}) - ln (x^{2} - 100) = ln (\frac{\frac{x + 10}{x - 10}}{x ^{2} - 100})

= ln (\frac{\frac{x + 10}{x - 10}}{x ^{2} - 100})

Simplify

\frac{\frac{x + 10}{x - 10}}{x ^{2} - 100} : \frac{1}{( x - 10 ) ^{2}}

= ln (\frac{1}{( x - 10 ) ^{2}})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln ((x - 10)^{2})

- lo g_{10} (3.98 \times 1 0^{- 9})

lo g_{5} (\frac{g}{125})

lo g_{b} (\frac{7}{8})

lo g_{2} (x^{4} y^{5})

lo g_{5} (u) + 6 lo g_{5} (v)

What is ln(x/(x-10))+ln((x+10)/x)-ln(x^2-100) ?
The solution to ln(x/(x-10))+ln((x+10)/x)-ln(x^2-100) is -ln((x-10)^2)