What is ln(((x^5))/(2y^6)) ?

The solution to ln(((x^5))/(2y^6)) is 5ln(x)-ln(2)-6ln(y)

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simplify ln(((x^5))/(2y^6))

simplify

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

5 ln (x) - ln (2) - 6 ln (y)

Solution steps

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

Apply log rule:

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

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

= ln (x^{5}) - ln (2 y^{6})

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= 5 ln (x) - ln (2 y^{6})

Apply log rule:

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

ln (2 y^{6}) = ln (2) + ln (y^{6})

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

Apply log rule:

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

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

= 5 ln (x) - (ln (2) + 6 ln (y))

- (ln (2) + 6 ln (y)) : - ln (2) - 6 ln (y)

= 5 ln (x) - ln (2) - 6 ln (y)

ln (z (z - 8)^{4})

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

- lo g_{10} (1.1 \cdot 1 0^{- 4})

ln (\frac{950}{1150})

ln (x^{2}) - ln (x^{4}) - 3 x

What is ln(((x^5))/(2y^6)) ?
The solution to ln(((x^5))/(2y^6)) is 5ln(x)-ln(2)-6ln(y)