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

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

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

simplify

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

ln (y + 4 x) - 6 ln (y - x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((y - x)^{6}) = 6 ln (y - x)

= ln (y + 4 x) - 6 ln (y - x)

2 lo g_{b} (x) - 3 lo g_{b} (y) + 4 lo g_{b} (z)

\frac{3}{2} ln (x^{10}) - \frac{4}{5} ln (2 y^{10})

- lo g_{10} (4.3 \cdot 1 0^{- 11})

ln (\frac{1 n}{1})

ln (5 \cdot 1 0^{- 4})

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