SOLUTION: Solve logxbase8 + log(1/6)base4 = 1/3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve logxbase8 + log(1/6)base4 = 1/3      Log On


   

Question 1134980: Solve logxbase8 + log(1/6)base4 = 1/3
Found 2 solutions by mathsolverplus, greenestamps:
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
.




If this answer has helped you and you need help on additional problems, please follow us on Instagram or message us via social media! We also help with SAT Math Questions!

[Best way to contact us] Instagram (@mathsolver.plus): https://www.instagram.com/mathsolver.plus/
Twitter (@MathSolverPlus): https://twitter.com/MathSolverPlus
Snapchat (@mathsolverplus)
Email: mathsolverplus@gmail.com

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


I read this as

log%288%2C%28x%29%29%2Blog%284%2C%281%2F6%29%29+=+1%2F3

Then

3log%288%2C%28x%29%29%2B3log%284%2C%281%2F6%29%29+=+1 (multiply by 3 to get a whole number on the right)

(convert to log base 2)

log%282%2C%28x%29%29%2B%283%2F2%29log%282%2C%281%2F6%29%29+=+log%282%2C%282%29%29

2%2Alog%282%2C%28x%29%29%2B3%2Alog%282%2C%281%2F6%29%29+=+2%2Alog%282%2C%282%29%29 (multiply by 2 again to clear fractions)

%28x%5E2%29%28%281%2F6%29%5E3%29+=+2%5E2 (convert to exponential form)
x%5E2%2F6%5E3+=+2%5E2
x%5E2+=+%282%5E2%29%286%5E3%29+=+%282%5E2%29%282%5E3%29%283%5E3%29+=+%282%5E5%29%283%5E3%29
x+=+12%2Asqrt%286%29