What is ln(x/(y^5z)) ?

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

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simplify ln(x/(y^5z))

simplify

ln (\frac{x}{y ^{5} z})

ln (x) - 5 ln (y) - ln (z)

Solution steps

ln (\frac{x}{y ^{5} z})

Apply log rule:

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

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

= ln (x) - ln (y^{5} z)

Apply log rule:

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

ln (y^{5} z) = ln (y^{5}) + ln (z)

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

Apply log rule:

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

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

= ln (x) - (5 ln (y) + ln (z))

- (5 ln (y) + ln (z)) : - 5 ln (y) - ln (z)

= ln (x) - 5 ln (y) - ln (z)

3 lo g_{10} (2) + 2 lo g_{10} (5)

ln (3.61 \cdot 1 0^{- 11})

lo g_{10} (\frac{x ^{15} y ^{17}}{z ^{13}})

ln (x (x + 1) (x + 2))

lo g_{6} (72) - lo g_{6} (144) - lo g_{6} (18)