Question

PRE-CALCULUS HELP WILL FAN AND MEDAL :)))))

Compare the graphs of the logarithmic functions f(x)=log_7 (x) and g(x)=log_4 (x). For what values of x is f=g, f>g, and f 8 years ago

Answer 1

f=g because you have to calculate the total of how ur going to start off.

Answer 2

hint \[\log_7(x)=\frac{\ln(x)}{\ln(7)}\]and \[\log_4(x)=\frac{\ln(x)}{\ln(4)}\]via "change of base"

Answer 3

So would you set them =, <, and > to each other and solve?

Answer 4

course you could always graph them with the computer you are on

Answer 5

True. How would I explain "how do you know" then lol

Answer 6

omg @satellite73 the 100 percenter... is that possible on openstudy?

Answer 7

what do you think is bigger, \[\log_4(16)\] or \[\log_7(16)\]?

Answer 8

All of my years doing logarithms and I did not know that log_7(x) = lnx/ln7 thanks satellite

Answer 9

yw

Answer 10

Log_4 would be bigger

Answer 11

yes of course,
now for what value of x do you think they are equal?

Answer 12

Well, 1 because that's where they intersect on the graph.

Answer 13

this is one number that gives the same answer no matter what the base of the log is
do you know that number?

Answer 14

oh. No lol sorry

Answer 15

oh yes, what you said, 1

Answer 16

Oh ok

Answer 17

\[\log_b(1)=0\] which is another way of saying \[b^0=1\]

Answer 18

no matter what \(b\) is

Answer 19

Gotcha. So would be the answer for the first part of the question, f=g?

Answer 20

would 1*

Answer 21

so we know they are equal if \(x=1\) since you get 0 for both

Answer 22

yes

Answer 23

and evidently if \(x>1\) you have \(\log_4(x)>\log_7(x)\) since you have to raise 4 to a bigger power

Answer 24

ok! And if x<1, then log 7(x) is bitter than log 4 (x)?

Answer 25

bitter and bigger too i think

Answer 26

they will of course both be negative

Answer 27

Ok, thanks!