Math F.4 Log

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2012-12-08 22:28:05 補充：
4. The last third line should be : (4logx - log5)(logx - 2log5) = 0

1.
2x+1 = log{base 3}(31(3^x)-36)
3^(2x+1)=31(3^x)-36
0=3(3^x)^2-31(3^x)+36
3^x=9 或 3^x=4/3
x=2 或 x=log(4/3)/log3
x=2 或 x=0.262

2.
logx /log7+ log49 /logx= 3
logx/log7 + 2log7/logx=3
[(logx)^2+2(log7)^2]/(log7logx)=3
(logx)^2+2(log7)^2=3log7logx
(logx)^2-3log7logx+2(log7)^2=0
logx=1.69019608 或 log x=0.84509804
x=49 或 x=7
3.
4 log{base x}27 - 3log{base 3}x = 5
12log3/logx-3logx/log3=5
12(log3)^2-3(logx)^2=5logxlog3
-3(logx)^2-5logxlog3+12(log3)^2=0
logx=-1.431363764 或 logx=0.636161673
x=0.0370 或 x=4.33

4.
2 log{base x}5 + 8log{base 25}x = 9
2log5/logx+4logx/log5=9
2(log5)^2+4(logx)^2=9logxlog5
4(logx)^2-9logxlog5+2(log5)^2=0
logx=2.3561638 或 logx=0.11438362
x=227 或 x=1.30