What is 6/5 ln(1-y/x)-1/5 ln(y/x+4) ?

The solution to 6/5 ln(1-y/x)-1/5 ln(y/x+4) is ln(((x-y)^{6/5}(y+4x)^{4/5})/(yx+4x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 6/5 ln(1-y/x)-1/5 ln(y/x+4)

simplify

\frac{6}{5} ln (1 - \frac{y}{x}) - \frac{1}{5} ln (\frac{y}{x} + 4)

ln (\frac{( x - y ) ^{\frac{6}{5}} ( y + 4 x ) ^{\frac{4}{5}}}{y x + 4 x ^{2}})

Solution steps

\frac{6}{5} ln (1 - \frac{y}{x}) - \frac{1}{5} ln (\frac{y}{x} + 4)

Apply log rule:

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

\frac{6}{5} ln (- \frac{y}{x} + 1) = ln ((- \frac{y}{x} + 1)^{\frac{6}{5}})

= ln ((- \frac{y}{x} + 1)^{\frac{6}{5}}) - \frac{1}{5} ln (\frac{y}{x} + 4)

Apply log rule:

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

\frac{1}{5} ln (\frac{y}{x} + 4) = ln ((\frac{y}{x} + 4)^{\frac{1}{5}})

= ln ((- \frac{y}{x} + 1)^{\frac{6}{5}}) - ln ((\frac{y}{x} + 4)^{\frac{1}{5}})

Apply log rule:

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

ln ((1 - \frac{y}{x})^{\frac{6}{5}}) - ln ((\frac{y}{x} + 4)^{\frac{1}{5}}) = ln \frac{( - \frac{y}{x} + 1 ) ^{\frac{6}{5}}}{( \frac{y}{x} + 4 ) ^{\frac{1}{5}}}

= ln \frac{( 1 - \frac{y}{x} ) ^{\frac{6}{5}}}{( \frac{y}{x} + 4 ) ^{\frac{1}{5}}}

Simplify

\frac{( 1 - \frac{y}{x} ) ^{\frac{6}{5}}}{( \frac{y}{x} + 4 ) ^{\frac{1}{5}}} : \frac{( x - y ) ^{\frac{6}{5}} ( y + 4 x ) ^{\frac{4}{5}}}{y x + 4 x ^{2}}

= ln (\frac{( x - y ) ^{\frac{6}{5}} ( y + 4 x ) ^{\frac{4}{5}}}{y x + 4 x ^{2}})

- lo g_{10} (6.8 \cdot 1 0^{4})

- ln (x) + \frac{1}{2} ln (b) - ln (c)

ln (\frac{e ^{9}}{19})

ln (\frac{x}{( x + 2 ) ( x + 3 )})

ln (\frac{x ^{2} x ^{2} + 3}{( x + 3 ) ^{8}})

What is 6/5 ln(1-y/x)-1/5 ln(y/x+4) ?
The solution to 6/5 ln(1-y/x)-1/5 ln(y/x+4) is ln(((x-y)^{6/5}(y+4x)^{4/5})/(yx+4x^2))