What is 1/4 ln(3x+1)-1/4 ln(x-1)+ln(k) ?

The solution to 1/4 ln(3x+1)-1/4 ln(x-1)+ln(k) is ln(\sqrt[4]{(3x+1)/(x-1)}k)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/4 ln(3x+1)-1/4 ln(x-1)+ln(k)

simplify

\frac{1}{4} ln (3 x + 1) - \frac{1}{4} ln (x - 1) + ln (k)

Solution steps

\frac{1}{4} ln (3 x + 1) - \frac{1}{4} ln (x - 1) + ln (k)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{4} ln (3 x + 1) = ln ((3 x + 1)^{\frac{1}{4}})

= ln ((3 x + 1)^{\frac{1}{4}}) - \frac{1}{4} ln (x - 1) + ln (k)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{4} ln (x - 1) = ln ((x - 1)^{\frac{1}{4}})

= ln ((3 x + 1)^{\frac{1}{4}}) - ln ((x - 1)^{\frac{1}{4}}) + ln (k)

Apply log rule:

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

ln ((3 x + 1)^{\frac{1}{4}}) - ln ((x - 1)^{\frac{1}{4}}) = ln (\frac{( 3 x + 1 ) ^{\frac{1}{4}}}{( x - 1 ) ^{\frac{1}{4}}})

= ln (\frac{( 3 x + 1 ) ^{\frac{1}{4}}}{( x - 1 ) ^{\frac{1}{4}}}) + ln (k)

Combine same powers :

Apply log rule:

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

ln (\frac{( e ^{2} )}{c ^{2} + 5})

ln (C k (e^{- a} - e^{- b}))

6 \cdot ln (\frac{3}{2}) - 4 \cdot ln (2) - 2 \cdot ln (\frac{6}{5})

- 2 \cdot ln (\frac{6}{5})

ln (\frac{3}{23}) + (\frac{4}{23})

What is 1/4 ln(3x+1)-1/4 ln(x-1)+ln(k) ?
The solution to 1/4 ln(3x+1)-1/4 ln(x-1)+ln(k) is ln(\sqrt[4]{(3x+1)/(x-1)}k)