What is ln((4y^5)/(x^2)) ?

The solution to ln((4y^5)/(x^2)) is 2ln(2)+5ln(y)-2ln(x)

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simplify ln((4y^5)/(x^2))

simplify

ln (\frac{4 y ^{5}}{x ^{2}})

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

Solution steps

ln (\frac{4 y ^{5}}{x ^{2}})

Apply log rule:

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

ln (\frac{4 y ^{5}}{x ^{2}}) = ln (4 y^{5}) - ln (x^{2})

= ln (4 y^{5}) - ln (x^{2})

Apply log rule:

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

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

= ln (4 y^{5}) - 2 ln (x)

Apply log rule:

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

ln (4 y^{5}) = ln (4) + ln (y^{5})

= ln (4) + ln (y^{5}) - 2 ln (x)

Apply log rule:

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

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

= ln (4) + 5 ln (y) - 2 ln (x)

ln (4) = 2 ln (2)

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

- lo g_{10} (2.9 \cdot 1 0^{- 3})

2 ln (3) - ln (2) - 2 ln (2)

- lo g_{10} (2 \cdot 1 0^{- 1})

4 lo g_{5} (x) - 3 lo g_{5} (y)

0.026 ln (0.095) + 0.416 ln (10)

What is ln((4y^5)/(x^2)) ?
The solution to ln((4y^5)/(x^2)) is 2ln(2)+5ln(y)-2ln(x)