What is ln(5/(7x^7y)) ?

The solution to ln(5/(7x^7y)) is ln(5)-ln(7)-7ln(x)-ln(y)

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simplify ln(5/(7x^7y))

simplify

ln (\frac{5}{7 x ^{7} y})

ln (5) - ln (7) - 7 ln (x) - ln (y)

Solution steps

ln (\frac{5}{7 x ^{7} y})

Apply log rule:

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

ln (\frac{5}{7 x ^{7} y}) = ln (5) - ln (7 x^{7} y)

= ln (5) - 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 (5) - (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 (5) - (ln (7) + 7 ln (x) + ln (y))

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

= ln (5) - ln (7) - 7 ln (x) - ln (y)

\frac{1}{2} ln (\frac{cos ( x ) - 1}{cos ( x ) + 1})

ln (\frac{7}{6}) + ln (\frac{5}{6})

9 ln (x + 3) - 2 ln (x)

2 lo g_{10} (tan (1 0^{\circ}) y^{\frac{1}{2}})

- lo g_{10} (1.5 x 1 0^{4})

What is ln(5/(7x^7y)) ?
The solution to ln(5/(7x^7y)) is ln(5)-ln(7)-7ln(x)-ln(y)