Question

Given that log 9 y=x, show that log y 3=1/2x.

Answer 1

does 1/2x mean 1 divided by 2x, or half x?

Answer 2

half, like 1 over 2x

Answer 3

- so do you know how you can changing the base of one logarithm on one different what is added ?

like for example : loga(b) = ? in base of b ,like logb(a)

Answer 4

- because log9(y)=x
- and you need to show that logy(3) = 1/(2x)

Answer 5

- right ?

Answer 6

- i know how to change the base
- and right.

Answer 7

yes and after that you need to write log9(y) in the form of log y (9)
- and from this you will ned to see that log y (3) = 1/2x

Answer 8

wait, i'm a bit slow.

Answer 9

ok

Answer 10

how about you show the steps?

Answer 11

how you write log9(y) in the form of log y(3) ?

Answer 12

- and can you tel me please that there is logy(3) = (1/2) x or 1/(2x) ?

Answer 13

Argh, now i don't know anything anymore. The question stated logy 3= 1/(2x)

Answer 14

- so one second possibile step if you begin it from

logy (3) =1/(2x) and here change x by log9 (y)

so than will get logy(3)= 1/(2log9 (y)

- but now to continue you need changing the base of 2log9 (y) on y

Answer 15

- okay, i got the first one.
- to change the base of 2log9 (y) on y....how?

Answer 16

\[\log_{9}y=x \]\[\log_{y}3=1/(2x) \]Change the base of \[\log_{y}3=1/(2x) \]\[\log_{9}3/\log_{9}y \]Substitute \[\log_{9}y=x \]\[\log_{9}3/x=1/(2x) \]\[\log_{9}3=x/(2x) \]\[\log_{9}3=1/2 \]\[9^{(1/2)}=3\]