Logarithmic and exponential functions

Question 1

log_a1

Answer 1

0

Question 2

log_aa^x

Answer 2

x

Question 3

a^log_ax

Answer 3

x

Question 4

What is the inverse of y=lnx?

Answer 4

y=e^x

Question 5

log_a(xy)

Answer 5

log_ax+log_ay

Question 6

log_a(x/y)

Answer 6

log_ax-log_ay

Question 7

log_a(x)^m

Answer 7

mlog_ax

Question 8

log_a(1/x)

Answer 8

-log_ax

Question 9

log_ba

Answer 9

log_ca/log_cb

Question 10

log_ba

Answer 10

1/log_ab

Question 11

How to sketch the curve of an exponential function in the form y=ke^nx+a

Answer 11

1. If n<0 (_ if n>0 _)
2. Find the intercepts
3. Consider when x -> ∞ and x -> -∞ to get the y-asymptote
4. y=a is an asymptote

Question 12

How to sketch the curve of a logarithmic function in the form y=kln(ax+b)

Answer 12

1. If k>0 /(, if k<0 (_
2. Find the intercepts
3. Consider y when x -> +∞
4. ax+b=0 therefore x=-b/a which is an asymptote