Question 253711: log(base3)((x^3)+3)=log(base9)(x^2) + log(base√3)(2)
*corrected version*
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! log(base3)((x^3)+3) = log(base9)(x^2) + log(base√3)(2)
-------------
Convert log(base9) to base 3
---
If log(base9)(x^2) = k
then 9^k = x^2
and (3)^(2k) = x^2
and log(base3)(x^2) = 2k
So, log(base9)x^2 = 2log(base3)x^2
---------------------------------------
Convert log(base sqrt(3))(2) to base 3
If log(base sqrt(3))(2) = k
then (sqrt(3)^k = 2
then (3)^(k/2) = 2
and log(base 3)2 = k/2
-------------------------------
Rewrite the problem:
log(3)(x^3+3) = 2log(3)x^2 + (1/2)log(3)2
---
log(3)(x^3+3) = log(3)x^4 + log(3)(sqrt(2))
---
log(3)(x^3+3) = log(3)[sqrt(2)*x^4]
---
x^3+3 = sqrt(2)*x^4
---
sqrt(2)x^4 - x^3 - 3 = 0
Graphing I get:
x = -1.0623..
x = 1.4310...
==============
Cheers,
Stan H.
|
|
|
