What is ln(7/(6x^6y)) ?

The solution to ln(7/(6x^6y)) is ln(7)-ln(6)-6ln(x)-ln(y)

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simplify ln(7/(6x^6y))

simplify

ln (\frac{7}{6 x ^{6} y})

ln (7) - ln (6) - 6 ln (x) - ln (y)

Solution steps

ln (\frac{7}{6 x ^{6} y})

Apply log rule:

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

ln (\frac{7}{6 x ^{6} y}) = ln (7) - ln (6 x^{6} y)

= ln (7) - ln (6 x^{6} y)

Apply log rule:

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

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

= ln (7) - (ln (x^{6}) + ln (y) + ln (6))

Apply log rule:

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

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

= ln (7) - (ln (6) + 6 ln (x) + ln (y))

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

= ln (7) - ln (6) - 6 ln (x) - ln (y)

lo g_{10} (\frac{x ^{2} - x - 12}{x})

lo g_{2} (10) - lo g_{2} (5) + lo g_{2} (11)

lo g_{10} (y) + lo g_{10} (18)

ln (\frac{13 x ^{8}}{y ^{5}})

What is ln(7/(6x^6y)) ?
The solution to ln(7/(6x^6y)) is ln(7)-ln(6)-6ln(x)-ln(y)