What is ln(7/(8x^8y)) ?

The solution to ln(7/(8x^8y)) is ln(7)-3ln(2)-8ln(x)-ln(y)

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simplify ln(7/(8x^8y))

simplify

ln (\frac{7}{8 x ^{8} y})

ln (7) - 3 ln (2) - 8 ln (x) - ln (y)

Solution steps

ln (\frac{7}{8 x ^{8} y})

Apply log rule:

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

ln (\frac{7}{8 x ^{8} y}) = ln (7) - ln (8 x^{8} y)

= ln (7) - ln (8 x^{8} y)

Apply log rule:

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

ln (8 x^{8} y) = ln (8) + ln (x^{8}) + ln (y)

= ln (7) - (ln (x^{8}) + ln (y) + ln (8))

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= ln (7) - (ln (8) + 8 ln (x) + ln (y))

ln (8) = 3 ln (2)

= ln (7) - (8 ln (x) + ln (y) + 3 ln (2))

- (3 ln (2) + 8 ln (x) + ln (y)) : - 3 ln (2) - 8 ln (x) - ln (y)

= ln (7) - 3 ln (2) - 8 ln (x) - ln (y)

lo g_{3} (x) + lo g_{3} (x + 7)

lo g_{2} (5) + lo g_{2} (7^{3}) + lo g_{2} (y)

- \frac{2 ln ( 3 )}{ln ( 2 )}

lo g_{2} (7) + lo g_{2} (x)

\frac{1}{2} lo g_{2} (5)

What is ln(7/(8x^8y)) ?
The solution to ln(7/(8x^8y)) is ln(7)-3ln(2)-8ln(x)-ln(y)