Solve the following bloody log equation!!!?

Question

log(subscript)3 (normal)x + 4log (subscript)x (normal)3 = 5

i still dont get it? the answer is 8, 81..
please show me in detail..!!

thanx everyone.. i'm goin look through each one.. thanx again..

Answer 1

mohanrao made one little mistake along the way, otherwise he would have gotten it on the nose.

log_3(x) + 4log_x(3) = 5
log_3(x) + 4[log_3(3)/log_3(x)] = 5
log_3(x) + 4[1/log_3(x)] = 5
(log_3(x))^2 + 4 = 5log_3(x)
(log_3(x))^2 - 5log_3(x) + 4 = 0; let u = log_3(x)

u^2 - 5u + 4 = 0
(u-4)(u-1) = 0
u = 4 and u = 1
log_3(x) = 4 and log_3(x) = 1
x = 3^4 and x = 3^1
x = 81 or x = 3

Answer 2

organic logs behave only like a number of different log. Say which you have the essential log (log base 10), the only way this log base 10 differs from ln is that the organic logs base is e . you could sparkling up the above equation by utilising only as you may with a typical log. attempt rewriting the question with the essential log and you ought to get the assumption of what to do . desire this facilitates.

Answer 3

I Like JD's and Linda's proofs. Very elegant!

By the way, why not just use the simple log relationship:

log base a of x = 1/log base x of a

Answer 4

change the second log to log base3
4log_x(3) = log_x(3^4) = log_x (81) = log_3(81)/log_3(x)= 4/log_3(x)

Now you have
log_3(x) + 4/log_3(x) = 5 multiply all terms by log_3(x) to clear denominator

[log_3(x)]^2 + 4 = 5log_3(x)
[log_3(x)]^2 -5log_3(x) + 4 = 0

factor
(log_3(x) -4)(log_3(x) -1) = 0

log_3(x) = 4 or log_3(x) = 1 convert to exponentials
x = 3^4 or x = 3^1
x = 81 or 3

Answer 5

use the base change rule

log(a) [to the base b] = log(a)/log(b) [to any other base]

change second term base from x to 3

log_3(x) + 4log_x(3) = 5

log_3(x) + 4[log_3(3)/log_3(x)] = 5

log_3(x) + 4[1/log_3(x)] = 5

=>log_3(x) + (1/log_3(x)^4) = 5

=>log_3[(x)*/x^4) = 5

=>log_3[1/x^3] = 5

5^3 = 1/x^3

x = 1/5

Answer 6

lnx / ln3 + 4ln3 / lnx = 5
Let u = lnx
u^2 - (5)(ln3)u + 4(ln3)^2 = 0
(u-ln3)(u-4ln3) = 0
u-ln3 = lnx - ln3 = 0, => x = 3
u-4ln3 = lnx - ln3^4 = 0, => x = 3^4 = 81

Answer 7

x = 3
This can be seen by simole inspection.

Answer 8

http://www.stepsedu.com/etutoring/demosession.php just click on this link and they will provide free session .just fill your name and in question write i want free demo session as kanpreesays ------------------------they will sure give you home work help they r very genious tutors .They make math so simple that i love to use it