Question

a^ [(log a)/(log b)] =3
b^[(logb)/(log a)]=81

Find a and b.
No options !
someone please solve !

Answer 1

just substitute the eqn of log b from 1 to 2

Answer 2

Didn't get you....

Answer 3

I think you'll need this log rule to solve:
Simpler example:
a^b = c
log(a^b)=log(c)
(b)(log a) = log(c)

Answer 4

So the first part of your question would become:
[ log(a) / log(b) ] log a = log3

Answer 5

k. fine then??

Answer 6

I think you did something wrong...

Answer 7

Proceed I just read the question wrong...then???

Answer 8

No = you're right. I did do something wrong. I cancelled the (log a) terms but that's wrong. They were both in the numerator. I deleted my posts above so as not to confuse someone else joining in. You can delete your posts too if you want.
Let me start over.

Take log of both sides to get.
[(log a)/(log b)] (log a) = log 3

[(log a)^2] / log b = log 3

Answer 9

Ya I got the answer...

Answer 10

yes, I think jam333 can do the same with the second one and replace to get the answer

Answer 11

So, after doing the same sort of thing), the second part gives you:
(log b)^2 / log 81 = log a
81 = 3^4
log 81 = 4 log 3

Answer 12

Let me confirm the answer. What values of a and b have you got??

Answer 13

I'm still calculating it.

Answer 14

k...fine.

Answer 15

not a beautiful number for b (if i didnt do wrong)

Answer 16

I didn't understand your answer @RadEn

Answer 17

i just got b, not yet for a :)

Answer 18

do you mean
\[b=3^{2^{\frac{ 4 }{ 3 }}}\]

Answer 19

b= 3^{2^(4/3)}

Answer 20

no, i got b like my drawing above :