First broadcast Autumn 2020
A-level catch up: Logs and Exponentials
Ben Ward-Cherrier
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Logs and exponentials
Exponential functions
I -> properties
Logarithmic functions
I -> properties
More sources & exercises.
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Exponential functions
y = 2x ...y = 3x ...y = 4x
Standard exponential is y = ex , where e ≈ 2.71828...
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Exponential function properties
ex1 ex2 = ex1 +x2
ex 1
x1 −x2
ex 2 = e
ekx = (ek )x
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Exponential functions - Worked example
James, Chap.2, Ex 72
Simplify
(a) (e2 )3 + e2 × e3 +(e3 )2
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Exponential functions - Worked example
James, Chap.2, Ex 72
Simplify
(a) (e2 )3 + e2 × e3 +(e3 )2
PAUSE THE VIDEO AND TRY THE EXAMPLE
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Exponential functions - Worked example
James, Chap.2, Ex 72
Simplify
(a) (e2 )3 + e2 × e3 +(e3 )2
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Logarithmic function
Natural logarithm ln : y = ex -> x = ln y
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Logarithmic function properties
ln x1 + ln x2 = ln x1 x2
ln x1 − ln x2 = ln xx21
ln xk = k ln x
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Logarithmic functions - Worked example
James, Chap.2, Ex 76
Express as a single logarithm:
(a) ln 14 − ln 21 + ln 6
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Logarithmic functions - Worked example
James, Chap.2, Ex 76
Express as a single logarithm:
(a) ln 14 − ln 21 + ln 6
PAUSE THE VIDEO AND TRY THE EXAMPLE
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
Logarithmic functions - Worked example
James, Chap.2, Ex 76
Express as a single logarithm:
(a) ln 14 − ln 21 + ln 6
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
What we have learned
ex = (ex )0
If y = ex then x = ln y
ex1 ex2 = ex1 +x2
ln x1 + ln x2 = ln x1 x2
e x1
= ex1 −x2
e x2
ln x1 − ln x2 = ln xx12
ekx = (ek )x
ln xk = k ln x
EngMaths I A-level catch up: Logs and Exponentials
First broadcast Autumn 2020
More information/examples/exercises
Basic YouTube videos: PatrickJMT (WARNING, external content)
Search for "circles", "ellipses", "parabolas" or "hyperbolas" for
additional explanations and worked examples.
More reading: See the James textbook:
James (& Dyke) Modern Engineering Mathematics 6th Ed
Read section 2.7.1 – 2.7.2
More exercises: James
Chap. 2: exercises 72,75,76,77
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