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
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