SECTION 6- EXPONENTIALS AND LOGARITHMS

Question 1

logs multiplication rule

Answer 1

logₐ x + logₐ y = logₐ xy

Question 2

logs subtraction rule

Answer 2

logₐ x - logₐ y = logₐ x/y

Question 3

log power/ indices rule

Answer 3

logₐ (xᵏ) = klogₐ x

Question 4

what is eˣ differentiated when it has a constant e.g. eᵏˣ

Answer 4

f (x) = eᵏˣ then f’(x) = keᵏˣ

Question 5

aˣ = n in log form

Answer 5

aˣ = n is equal to logₐ n = x

Question 6

what does the graph of eˣ look like

Answer 6

• like an exponential function

- it’s gradient is exactly the same as the original function

Question 7

what is the answer to logₐ a

Answer 7

logₐ a = 1

Question 8

what is eˣ differentiated

Answer 8

f (x) = f’(x) = eˣ

Question 9

what is the answer to logₐ 1

Answer 9

logₐ 1 = 0

Question 10

how to solve an equation using logs in this format e.g. f (x) = g (x)

Answer 10

logₐ f (x) = logₐ g (x)

Question 11

relationship between lnx graphs and eˣ

Answer 11

• the graph of lnx is a reflection of the graph y = eˣ in the line y = x
• so lnx is only defined for positive values of x

Question 12

what is the answer to eˡⁿˣ

Answer 12

eˡⁿˣ = ln (eˣ) = x

Question 13

what is lnx equal to e.g. lnx =

Answer 13

lnx = logₑ x

Question 14

what will the graph of log y against log x look like if y = axⁿ

Answer 14

• it will be a straight line with gradient n and vertical intercept (the y intercept) of log a

Question 15

what is an asymptote

Answer 15

• a line a graph approaches w/o touching e.g. the asymptote of eˣ is 0