Core 3 - e^x and lnx

Question 1

What is the relationship between e and ln? How is this represented on a graph?

Answer 1

They are opposite functions, like sin and sin-1. They are reflections in y=x of each other.

Question 2

What is the log rule for addition of lns?

Answer 2

ln(a) + ln(b) = ln(ab)

Question 3

What is the log rule for subtraction of lns?

Answer 3

ln(a) - ln(b) = ln(a/b)

Question 4

What is the log rule for manipulating powers of lns?

Answer 4

ln(x^k) =kln(x)

Question 5

What is the derivative of e^f(x)

Answer 5

f’(x) e^f(x)

Question 6

What is the derivative of ln(x)

Answer 6

f’(x)/f(x)

Question 7

Why must a ln of x be in a modulus?

Answer 7

Ln of a negative value is not defined, so the modulus allows the positive integer to be defined.

Question 8

What must you ensure is isolated before you ln an equation?

Answer 8

e^x must be isolated to find x on its own.

Question 9

What are the steps to differentiate, by inspection, y=e^f(x)

Answer 9

Differentiate f(x) to get f’(x)
Bring this in front of the expression
Keep e^f(x) as it is
=> f’(x) (e^f’(x))