What is expand ln((7xy^3)/z) ?

The solution to expand ln((7xy^3)/z) is ln(7)+ln(x)+3ln(y)-ln(z)

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expand ln((7xy^3)/z)

expand

ln (\frac{7 x y ^{3}}{z})

ln (7) + ln (x) + 3 ln (y) - ln (z)

Solution steps

ln (\frac{7 x y ^{3}}{z})

Apply log rule:

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

ln (\frac{7 x y ^{3}}{z}) = ln (7 x y^{3}) - ln (z)

= ln (7 x y^{3}) - ln (z)

Apply log rule:

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

ln (7 x y^{3}) = ln (7) + ln (x) + ln (y^{3})

= ln (7) + ln (x) + ln (y^{3}) - ln (z)

Apply log rule:

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

ln (y^{3}) = 3 ln (y)

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

4 lo g_{8} (a) + 16 lo g_{8} (b)

3 ln ∣ x + 3 ∣ - ln ∣ x - 3 ∣ + C

7 lo g_{5} (6 e) + 5 lo g_{5} (2 e)

20 \cdot lo g_{10} (\frac{1}{2 π ^{0} + 1})

- (\frac{5}{11}) \cdot ln (\frac{5}{11})

What is expand ln((7xy^3)/z) ?
The solution to expand ln((7xy^3)/z) is ln(7)+ln(x)+3ln(y)-ln(z)