What is ln(y-2)-1/3 ln(y-1) ?

The solution to ln(y-2)-1/3 ln(y-1) is ln(((y-2)(y-1)^{2/3})/(y-1))

Popular >

simplify ln(y-2)-1/3 ln(y-1)

simplify

ln (y - 2) - \frac{1}{3} ln (y - 1)

ln (\frac{( y - 2 ) ( y - 1 ) ^{\frac{2}{3}}}{y - 1})

Solution steps

ln (y - 2) - \frac{1}{3} ln (y - 1)

Apply log rule:

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

\frac{1}{3} ln (y - 1) = ln ((y - 1)^{\frac{1}{3}})

= ln (y - 2) - ln ((y - 1)^{\frac{1}{3}})

Apply log rule:

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

ln (y - 2) - ln ((y - 1)^{\frac{1}{3}}) = ln (\frac{y - 2}{( y - 1 ) ^{\frac{1}{3}}})

= ln (\frac{y - 2}{( y - 1 ) ^{\frac{1}{3}}})

Simplify

\frac{y - 2}{( y - 1 ) ^{\frac{1}{3}}} : \frac{( y - 2 ) ( y - 1 ) ^{\frac{2}{3}}}{y - 1}

= ln (\frac{( y - 2 ) ( y - 1 ) ^{\frac{2}{3}}}{y - 1})

3 ln (4) - ln (\frac{4}{3})

\frac{1}{10} ln (\frac{4}{3})

\frac{1}{- 0.06437} ln (\frac{1}{20})

ln (\frac{100}{0.2})

ln ((n + 1)^{2}) - ln (n^{2})

What is ln(y-2)-1/3 ln(y-1) ?
The solution to ln(y-2)-1/3 ln(y-1) is ln(((y-2)(y-1)^{2/3})/(y-1))