中四數學難題

Consider the following table







x
6^x
11^2x
6^x+11^2x-199

1
6
121
-72

2
36
14641
14478

1.5
14.69694
1331
1146.696938

1.25
9.390507
401.3116
211.7021071

1.125
7.5062
220.3604
28.86659514

1.0625
6.710976
163.2899
-28.99907376

1.09375
7.09746
189.6909
-2.211639637

1.109375
7.298969
204.4514
12.75033712

1.101563
7.197509
196.9329
5.130401713

1.097656
7.147309
193.278
1.425289902

1.095703
7.122341
191.476
-0.401618264
The value of x is between 1.095703 and 1.097656
x = 1.10 corr. to 3 sig. fig.

Ans :
6^x+11^(2x)=199
x(log6)+(2x)(log11)=log199
x(log6+2log11)=log199
x=log199/(log6+2log11)
x=0.804