Logs And Exponentials B1 Ch14

Question 1

What is an exponential function?

Answer 1

When y=a^x

Question 2

Where does the graph of y=a^x cross the y axis?

Answer 2

At y=1

Question 3

What is the reflection of y=2^x in the y axis?

Answer 3

y=(1/2)^x

Question 4

What is the special mathematical property that exponential functions have?

Answer 4

The graphs of their gradient functions are similar in shape to the normal graph

Question 5

What is special about e?

Answer 5

The gradient function of e is exactly the same as the original function

Question 6

If y=e^kx what does dy/dx=?

Answer 6

dy/dx=ke^kx

Question 7

What is the inverse of an exponential function?

Answer 7

A log

Question 8

How can a^x=n be written in log form?

Answer 8

Loga(n)=x

Question 9

What is the log multiplication law?

Answer 9

Loga(x)+Loga(y)=loga(xy)

Question 10

What is the log division law?

Answer 10

Loga(x)-loga(y)=loga(x/y)

Question 11

What is log power law?

Answer 11

Loga(x^k)=kloga(x)

Question 12

When loga(a)=1 what can a not be equal to?

Answer 12

a cannot be equal to 1

Question 13

When loga(1)=0 what can a not equal?

Answer 13

a cannot be 1

Question 14

When f(x)=g(x) how can they be written in terms of logs?

Answer 14

Loga(fx)=loga(gx)

Question 15

What is the graph of y=ln x

Answer 15

The reflection of the graph of y=e^x in the line y=x

Question 16

What is e^(lnx) equal to?

Answer 16

e^(lnx)=ln(e^x)=x

Question 17

Solve e^x=5 to give x in exact form

Answer 17

e^x=5 ln(e^x)=ln5 x=ln5

Question 18

Solve lnx=3 to give x in exact form

Answer 18

lnx=3 e^(lnx)=e³ x=e³

Question 19

How can the graph y=axⁿ be put into the form y=mx+c

Answer 19

y=axⁿ Log(y)=log(ax)ⁿ Log(y)=log(a)+log(x)ⁿ Log(y)=log(a)+nlog(x)