SOLUTION: I have 3 to the sqrt of 21x. Which value of x makes the expression equivalent to 12 to the sqrt of 21? I don't remember how to work this. How does the number in front play in?? Tha

Algebra ->  Finance -> SOLUTION: I have 3 to the sqrt of 21x. Which value of x makes the expression equivalent to 12 to the sqrt of 21? I don't remember how to work this. How does the number in front play in?? Tha      Log On


   

Question 1012590: I have 3 to the sqrt of 21x. Which value of x makes the expression equivalent to 12 to the sqrt of 21? I don't remember how to work this. How does the number in front play in?? Thanks
Found 2 solutions by Fombitz, fractalier:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28sqrt%2821x%29%29=12%5Esqrt%2821%29
So then take the log base 3 of both sides.
sqrt%2821x%29=log%283%2C%2812%5Esqrt%2821%29%29%29
Square both sides,
21x=%28log%283%2C%2812%5Esqrt%2821%29%29%29%29%5E2
Divide by 21,
x=%28log%283%2C%2812%5Esqrt%2821%29%29%29%29%5E2%2F21 or
x=%28log%28%2812%5Esqrt%2821%29%29%29%29%5E2%2F%2821%2A%28log%28%283%29%29%29%5E2%29 or approximately
x=5.116

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
I'm thinking you mean
3%5E%28sqrt%2821x%29%29+=+12%5E%28sqrt%2821%29%29
If so, I think I would take the log of both sides and get
sqrt(21x)*log3 = sqrt(21)*log12
sqrt(21x)*log3 = sqrt(21)*(log4 + log3)
sqrt(x)*log3 = log4 + log3
sqrt(x) = (log4 + log3) / log3
so that
x = [(log4 + log3) / log3]^2 = 5.116