What is ln((5x^4y)/(7z)) ?

The solution to ln((5x^4y)/(7z)) is ln(5)+4ln(x)+ln(y)-ln(7)-ln(z)

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simplify ln((5x^4y)/(7z))

simplify

ln (\frac{5 x ^{4} y}{7 z})

ln (5) + 4 ln (x) + ln (y) - ln (7) - ln (z)

Solution steps

ln (\frac{5 x ^{4} y}{7 z})

Apply log rule:

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

ln (\frac{5 x ^{4} y}{7 z}) = ln (5 x^{4} y) - ln (7 z)

= ln (5 x^{4} y) - ln (7 z)

Apply log rule:

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

ln (5 x^{4} y) = ln (5) + ln (x^{4}) + ln (y), ln (7 z) = ln (7) + ln (z)

= ln (5) + ln (x^{4}) + ln (y) - (ln (z) + ln (7))

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= ln (5) + 4 ln (x) + ln (y) - (ln (7) + ln (z))

- (ln (7) + ln (z)) : - ln (7) - ln (z)

= ln (5) + 4 ln (x) + ln (y) - ln (7) - ln (z)

\frac{- ln ( \frac{2}{3} ) - \frac{1}{3}}{3} + 9 ln (\frac{2}{3}) + 3 + \frac{3}{2} + \frac{1}{9} + \frac{1}{36}

ln (\frac{3.635 \cdot 1 0 ^{- 3}}{1.29 \cdot 1 0 ^{- 3}})

ln (25 e^{25}) - 4 ln (5 e^{5}) + e^{l n (25)}

ln (\frac{- 4}{1 + i})

7 lo g_{10} (x) - 12 lo g_{10} (y)

What is ln((5x^4y)/(7z)) ?
The solution to ln((5x^4y)/(7z)) is ln(5)+4ln(x)+ln(y)-ln(7)-ln(z)