What is ln((2x^5)/(y^7)) ?

The solution to ln((2x^5)/(y^7)) is ln(2)+5ln(x)-7ln(y)

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simplify ln((2x^5)/(y^7))

simplify

ln (\frac{2 x ^{5}}{y ^{7}})

ln (2) + 5 ln (x) - 7 ln (y)

Solution steps

ln (\frac{2 x ^{5}}{y ^{7}})

Apply log rule:

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

ln (\frac{2 x ^{5}}{y ^{7}}) = ln (2 x^{5}) - ln (y^{7})

= ln (2 x^{5}) - ln (y^{7})

Apply log rule:

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

ln (y^{7}) = 7 ln (y)

= ln (2 x^{5}) - 7 ln (y)

Apply log rule:

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

ln (2 x^{5}) = ln (2) + ln (x^{5})

= ln (2) + ln (x^{5}) - 7 ln (y)

Apply log rule:

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

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

= ln (2) + 5 ln (x) - 7 ln (y)

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n^{2} (x)} + ln (3)

2 lo g_{10} (y) + lo g_{10} (x)

\frac{1}{2} lo g_{a} (x) + 5 lo g_{a} (y) - 3 lo g_{a} (x)

3 lo g_{10} (x^{3} y) + 2 lo g_{10} (y z^{2})

2 lo g_{10} (x) - 5 lo g_{10} (x + 1)

What is ln((2x^5)/(y^7)) ?
The solution to ln((2x^5)/(y^7)) is ln(2)+5ln(x)-7ln(y)