SOLUTION: log(base3)((x^3)+3)=log(base9)(x^2) + log(base√3)(2)
*corrected version*
Algebra.Com
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.
RELATED QUESTIONS
Solve: log [base3] (x^3 +3) = log [base9] (x^2) + log [base√3] 2
*√;... (answered by richwmiller)
2/3 log... (answered by lwsshak3)
log base3 (x+2)+log... (answered by ankor@dixie-net.com)
log(6x-3)base... (answered by harpazo)
solve the equation.
log(base... (answered by lwsshak3)
Please help.
log base3(x-2)+log base3(x+4)=3
e^x+5=8
(answered by Earlsdon)
Use log properties to combine the following log expression as a single logarithm.... (answered by lwsshak3)
express as a logarithm of a single number:
1. log basex 20 + logbasex 2
2. 3 log... (answered by lwsshak3)
2log base3(x+4)=log base 3 9+2
solve for... (answered by solver91311)