What is ln((7x^5)/(y^3)) ?

The solution to ln((7x^5)/(y^3)) is ln(7)+5ln(x)-3ln(y)

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simplify ln((7x^5)/(y^3))

simplify

ln (\frac{7 x ^{5}}{y ^{3}})

ln (7) + 5 ln (x) - 3 ln (y)

Solution steps

ln (\frac{7 x ^{5}}{y ^{3}})

Apply log rule:

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

ln (\frac{7 x ^{5}}{y ^{3}}) = ln (7 x^{5}) - ln (y^{3})

= ln (7 x^{5}) - ln (y^{3})

Apply log rule:

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

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

= ln (7 x^{5}) - 3 ln (y)

Apply log rule:

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

ln (7 x^{5}) = ln (7) + ln (x^{5})

= ln (7) + ln (x^{5}) - 3 ln (y)

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= ln (7) + 5 ln (x) - 3 ln (y)

ln (9616) - 2 ln (96)

4 ln (x) + 6 ln (y) + 3 ln (z)

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

\frac{1}{2} ln (\frac{4 + 7}{3})

ln (\frac{1}{32})

What is ln((7x^5)/(y^3)) ?
The solution to ln((7x^5)/(y^3)) is ln(7)+5ln(x)-3ln(y)