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How do you simplify ln e^2? - Socratic 2 ln(x) is asking e to the power of what is x In this case, e to the power of 2 is e^2 thus, ln(e^2)=2 Another way is using the property of logarithms that says ln(a^b)=b*ln(a) In this case, a=e and b=2 Thus, ln(e^2)=2*ln(e)=2*1=2
The Natural Base e - Precalculus - Socratic e is the coordinate on the x -axis where the area under y = 1 x and above the axis, from 1 to e is 1 e = lim m→∞ (1 + 1 m)m e ≈ 2 71828 it is an irrational number, so its decimal expansion neither terminates nor goes into a cycle (It is also transcendental which, among other things, means it cannot be written using finitely many
How to express e^(2-i) in the form a + ib? - Socratic I would write it as: e^2*e^(-1i) Then I will use the conversion from expoential to trigonometric form of a complex number as: re^(-itheta)=r[cos(theta)-isin(theta)] with theta=1 in radians; and convert it into rectangular form getting: e^2[cos(1)-isin(1)]~=4-6i
How do you simplify e^-2*e^6? - Socratic Explanation: We can use the law of exponents to simplify this expression Note that an ⋅ am = am+n In this case, we do the same: e−2 ⋅ e6 = e−2+6 = e4 If you like, you can think of e−2 as 1 e2 Alternatively you can write e6 e2 = e4 e^ (-2) * e^ (6) = e^4 We can use the law of exponents to simplify this expression
How do you find the integral of #e^(x^2)#? - Socratic Since ex = 1 + x + x2 2! + x3 3! +⋯ = 1 + x + x2 2 + x3 6 +⋯ (for all x), it follows that ex2 = 1 +x2 + x4 2 + x6 6 + ⋯ (for all x) It is valid in this example to now integrate term-by-term (the result is true for all x): ∫ex2dx = ∫(1 + x2 + x4 2 + x6 6 +⋯)dx = C + x + x3 3 + x5 10 + x7 42 +⋯ Alternatively, you can also give
How does e (2. 718) help apply to applications implications . . . - Socratic Jun 2, 2018 Euler's number, e, has few common real life applications Instead, it appears often in growth problems, such as population models It also appears in Physics quite often As for growth problems, imagine you went to a bank where you have 1 dollar, pound, or whatever type of money you have The bank offers you 100% interest every year