Question

How does 9^((log 5)/(log 3)) equal 25?!?

Answer 1

Can you please explain? I would be soooooo thankful if somebody could help me

Answer 2

change of base formula

Answer 3

\[3^x=5\iff x=\frac{\log(5)}{\log(3)}\]

Answer 4

i know that log5/log is change of base but how do you raise 9 to a log

Answer 5

By the way, thank you sooo mcuch for wanting to help me :)

Answer 6

so if \(3^x=5\) then \(9^x=25\)

Answer 7

that is clear right?

Answer 8

But why 3^x where do you get that from im sooo sorry im really confused i just want to understand hw to do it

Answer 9

ok lets go slow

Answer 10

thank you :D

Answer 11

is it clear that
\[b^x=A\iff x=\frac{\log(A)}{\log(b)}\]?

Answer 12

yes :)

Answer 13

ok so if we put \(b=3, A=5\) we have
\[3^x=5\iff x=\frac{\log(5)}{\log(3)}\] right?

Answer 14

yes, im following :D

Answer 15

so if \(3^x=5\) then \(9^x=25\) yes?

Answer 16

YES cause 9 is 3 squared right?!

Answer 17

as \(3=3^2\) so \(9^x=3^{2x}=5^2=25\)

Answer 18

THANK YOU SO MUCH!! ahhh you helped me so much

Answer 19

seriosuly :D

Answer 20

or to make it even more obvious
\[3^x=5\] so
\[9^x=(3^2)^x=(3^x)^2=5^2=25\]

Answer 21

Thank you :) you are awesome

Answer 22

and so if
\[3^{\frac{\log(5)}{\log(3)}}=5\] then
\[9^{\frac{\log(5)}{\log(3)}}=5^2=25\]

Answer 23

yw

Answer 24

:)

Answer 25

btw there might be some other way to see this
with logs there is usually more than one way to skin a cat

Answer 26

got it PERFECTLY yes, logs have many ays of a pproaching problems but this was more than enough