SOLUTION: 2/log(base x)4 + 3/log(base 4)x = 7

Question 720760: 2/log(base x)4 + 3/log(base 4)x = 7
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
2/log(base x)4 + 3/log(base 4)x = 7
convert to Base 10
2/(log4/logx)+3/(logx/log4)=7
2logx/log4+3log4/logx=7
LCD:(logx)(log4)
2(logx)^2+3(log4)^2=7log4logx
log4≈.60206
2(logx)^2+1.08743=4.21442logx
2(logx)^2-4.21442logx+1.08743=0
solve for logx using quadratic formula:
logx=.30102
x=10^.30102
x≈2
or
logx=1.80618
x=10^1.80618
x≈64
..
Check:
for x=2
2/log(base x)4+3/log(base 4)x
=2/log2(4) + 3/log4(2)
=2/2+3/(1/2)
=1+6=7
..
for x=64
2/log(base x)4+3/log(base 4)x
=2/log64(4) + 3/log4(64)
=2/(1/3)+3/3
=6+1=7
ans:
x=2 or 64

RELATED QUESTIONS
Log base 2 (4)log base 2 (x) + log base 2 (7) =3 (answered by Fombitz,MathTherapy)

4^log 3 base 9 + 9^log 4 base 2 =log^log 8.3 base... (answered by Alan3354)

log( base 2) x + log (base 4) x =... (answered by josmiceli)

Solve for x: A.) Log(base 3)4 + log(base 3)5 = log(base 3)(4x+5) B.)log(base 7)6... (answered by algebrapro18)

log base 2 (3x+2) -log base 4... (answered by stanbon)

log(base 4)(x-9)=2 log(base 4)z + log(base... (answered by ewatrrr)

Please help! Write 3 log base 5 (x-2) - 2 log base 5 (x+7) + 4 log base 5(x+9) - log... (answered by lwsshak3)

solve: log 4 base 2 - log (x+3) base 2 = log 8 base... (answered by lwsshak3)

how do you solve log base 4 (log base 3 (log base 2 of X)) = 0?? (answered by stanbon)