Exponentials and logarithms

Question 1

What does the graph of y=aˣ look like for a>1?

Answer 1

It has an asymptote at y=0 and crosses the y axis at (0,1). It is continually increasing. As x tends to infinity, y tends to infinity, and as x tends to minus infinity, y tends to 0

Question 2

What does the graph of y=aˣ look like for 0<a<1?

Answer 2

It has an asymptote at y=0 and crosses the y axis at (0,1). It is continually decreasing. As x tends to infinity, y tends to 0, and as x tends to minus infinity, y tends to infinity

Question 3

How can logₐ(b)=c be rewritten using powers?

Answer 3

aᶜ=b

Question 4

How can logₐ(bc) be rewritten according to the multiplication law?

Answer 4

logₐ(b)+logₐ(c)

Question 5

How can logₐ(b/c) be rewritten according to the division law?

Answer 5

logₐ(b)-logₐ(c)

Question 6

How can logₐ(bᶜ) be rewritten according to the power law?

Answer 6

c*logₐ(b)

Question 7

How can logₐ(1/b) be rewritten?

Answer 7

-logₐ(b)

Question 8

How can aᵇ=c be rewritten with b as the subject?

Answer 8

Take logarithms of both sides to give log(aᵇ)=log(c), and then apply the power rule to give b*log(a)=log(c). Then divide by log(a) to give b=log(c)/log(a)

Question 9

How can logₐ(b) be rewritten in terms of logarithms with base r according to the change of base rule?

Answer 9

logᵣ(b)/logᵣ(a)

Question 10

How can 1/logₐ(x) be rewritten?

Answer 10

logₓ(a)