What is ln((e^3)*(x^3)*(y^4)) ?

The solution to ln((e^3)*(x^3)*(y^4)) is 3+3ln(x)+4ln(y)

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simplify ln((e^3)(x^3)(y^4))

simplify

ln ((e^{3}) \cdot (x^{3}) \cdot (y^{4}))

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

Solution steps

ln ((e^{3}) (x^{3}) (y^{4}))

Apply log rule:

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

ln ((e^{3}) (x^{3}) (y^{4})) = ln (e^{3}) + ln (x^{3}) + ln (y^{4})

= ln (e^{3}) + ln (x^{3}) + ln (y^{4})

Apply log rule:

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

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

= 3 ln (e) + ln (x^{3}) + ln (y^{4})

Apply log rule:

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

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

= 3 ln (e) + 3 ln (x) + ln (y^{4})

Apply log rule:

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

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

= 3 ln (e) + 3 ln (x) + 4 ln (y)

3 ln (e) = 3

= 3 + 3 ln (x) + 4 ln (y)

\frac{5}{4} ln (x) - \frac{7}{2 x} - \frac{5}{4} ln (x + 2) + C

lo g_{10} ((tan (x))^{\circ}) 2 x

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

- lo g_{10} (2.7 \cdot 1 0^{- 7})

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

What is ln((e^3)*(x^3)*(y^4)) ?
The solution to ln((e^3)*(x^3)*(y^4)) is 3+3ln(x)+4ln(y)