Question

f(x)=x
: f(x)=e^x
: f(x)=5^x
: f(x)=ln(x)
: f(x)=log5(x)

Answer 1

: f(x)=log5(x) is it that you got ?

Answer 2

yeah

Answer 3

f(x) = x is easy.

For 5^x and e^x, do you remember the general shape of an exponential graph? They grow rapidly as x increases. 5^x will grow faster, since it's 5*5*5 etc, instead of e*e*e (which is about 2.78)

Similarly, log base 5 x will grow slower than ln x.

Answer 4

okay i do remember it this is what i got but i was not sure if it was correct f(x)= yellow, e^x+pink, 5^x=green

Answer 5

wait no 5^x is red and ln(x) is red and the green one is log_5(x)

Answer 6

Close, but the function that grows fastest/rises the fastest (as x gets larger) will be the 5^x.

Log5 (x) will be the function that rises the slowest as x gets larger.

Answer 7

oh hmm so then the ones that are going up are 5^x and log5(x) but is ln(x) the pink one

Answer 8

5^x will be the one that rises fastest, log5 x will be the one that rises *slowest* as x grows.

You could plug in x=1 into each equation to help you decide, too.

Answer 9

oh ok i should have thought of that plugging in x values is easier for me thanks:)

Answer 10

Then you can plug in x=2 also, since some of them are equal at x=1

Answer 11

alright i have one left ill plug in values for that one Thanks again!

Answer 12

Probably been a while since you've done them (pre-calc probably) but the log and exponential functions are inverses of each other - this is why they're reflected about the line y=x

e^x is the inverse of ln x and vice versa

5^x is the inverse of log5 x and vice versa