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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

\frac{60}{2.2} ln (\frac{0.116}{0.039})

ln (\frac{3 x + 5}{2 x + 1})

lo g_{e} (\frac{x ^{3} - 3 x + 9}{x ^{3}})

- lo g_{10} (4.29 \cdot 1 0^{- 6})

- ln (\frac{16}{15})

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