What is ln(9/(7x^7y)) ?

The solution to ln(9/(7x^7y)) is 2ln(3)-ln(7)-7ln(x)-ln(y)

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simplify ln(9/(7x^7y))

simplify

ln (\frac{9}{7 x ^{7} y})

2 ln (3) - ln (7) - 7 ln (x) - ln (y)

Solution steps

ln (\frac{9}{7 x ^{7} y})

Apply log rule:

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

ln (\frac{9}{7 x ^{7} y}) = ln (9) - ln (7 x^{7} y)

= ln (9) - 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 (9) - (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 (9) - (ln (7) + 7 ln (x) + ln (y))

ln (9) = 2 ln (3)

= 2 ln (3) - (7 ln (x) + ln (y) + ln (7))

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

= 2 ln (3) - ln (7) - 7 ln (x) - ln (y)

ln (\frac{8}{2})

lo g_{10} (\frac{x y}{z})

lo g_{a} (m) - lo g_{a} (n) - lo g_{a} (t)

lo g_{5} ((m + n) \cdot p)

lo g_{9} (k^{2} - 81) - lo g_{9} (k - 9)

What is ln(9/(7x^7y)) ?
The solution to ln(9/(7x^7y)) is 2ln(3)-ln(7)-7ln(x)-ln(y)