Answer in 60

Answered By: Ashton Green Date: created: Aug 29 2022


log(2, x)

Exact result



x = 1

Properties as a real function

{x element R : x data-lazy-src=0} (all positive real numbers)”>


d/dx(log(2, x)) = 1/(x log(2))

Indefinite integral

integral log(x)/log(2) dx = (x (log(x) - 1))/log(2) + constant(assuming a complex-valued logarithm)

Alternative representation

log(2, x) = log(x)/log(2)

Series representations

log(2, x) = (2 π floor(arg(x - ξ)/(2 π)) - i log(ξ) + i sum_(k=1)^∞ ((-1)^k (x - ξ)^k ξ^(-k))/k)/(2 π floor(arg(2 - ξ)/(2 π)) - i log(ξ) + i sum_(k=1)^∞ ((-1)^k (2 - ξ)^k ξ^(-k))/k) for ξ<0

Definite integral

integral_0^1 log(x)/log(2) dx = -1/log(2)≈-1.4427

Key moments in video
From 00:06 — Graph a Log Function

From 06:56 — The Transformed Graph

From 09:20 — Y-Intercept

From 09:45 — Find the Y Intercept

From 10:41 — Find X-Intercept

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Answered By: Owen Gonzalez Date: created: Sep 15 2022

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