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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

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

- (ln (7) + 7 ln (x) + ln (y)) : - ln (7) - 7 ln (x) - ln (y)

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

ln (\frac{x}{3 y})

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

ln (2 x) - ln (3 y)

2 [ln (x) - ln (x + 1) - ln (x - 1)]

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