Get me the solution?

Question

Ok so we are learning logarithms in college and i need the answer or solution to this problem, i will write in the way we pronuonce it :

log of x to the base ( square root of 3 ) + log of x to the base (3) + log of x to the base (1/3) = 4


Then find x

Answer 1

I'm going to use the following rules.
1. log base a of b = ln(a) / ln(b)
2. log base a of b^c = c times log base a of b
3. ln is the log base e

So let's see what we can do.

ln(x) / ln(3^(1/2)) + ln(x) / ln(3) + ln(x) / ln(1/3) = 4
ln(x) / ((1/2)ln(3)) + ln(x) / ln(3) + ln(x) / ln(3^(-1)) = 4
ln(x) / ((1/2)ln(3)) + ln(x) / ln(3) + ln(x) / ((-1)ln(3)) = 4
(2)ln(x) / ln(3) + ln(x) / ln(3) - ln(x) / ln(3) = 4
(2)ln(x) + ln(x) - ln(x) = (4)ln(3)
(2)ln(x) = (4)ln(3)
ln(x) = (2)ln(3)
ln(x) = ln(3^2)
x = 9

Answer 2

You have to know that
log(a) to the base b =
log(a) to the base g / log(b) to the base g
with g >0 and not g=1

When I do not mention the base it is 10, the common log.

log of x to the base ( square root of 3 ) + log of x to the base (3) + log of x to the base (1/3) = 4 ==>
log(x) / log(V3) + log(x) / log(3) + log(x) / log(1/3) = 4 ==>
log(x) * {1 / log(V3) + 1 / log(3) + 1 / log(1/3)} = 4 ==>
log(x) = 4 / {1 / log(V3) + 1 / log(3) + 1 / log(1/3)} ==>
log(x) = 4 / {2 / log(3) + 1 / log(3) - 1 / log(3)} ==>
log(x) = 4 / {2 / log(3)} ==>
log(x) = 2 * log(3) = log(9) ==> x = 9

Check:
log(9) / log(V3) + log(9) / log(3) + log(9) / log(1/3) =
2log(3) / (1/2)log(3) + 2log(3) / log(3) + 2log(3)/(-log(3)) =
4 + 2 - 2 = 4 this is alright
Th

Answer 3

i think it's 1.3333...but i'm not sure cuz i'm gonna b a freshman. but if log 3*=0..find x. 3 to the zeroth power = x...so x=1

Answer 4

sorry not that smart good luck that makes you think way to hard.