SOLUTION: roots of 2^x + 12(2)^-x = 7

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Question 934270: roots of 2^x + 12(2)^-x = 7
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2%5Ex+%2B+12%282%29%5E%28-x%29+=+7+
Multiply both sides by +2%5Ex+
+2%5E%28+2x+%29+%2B+12+=+7%2A2%5Ex+
Let +z+=+2%5Ex+
+z%5E2+-+7z+%2B+12+=+0+
+%28+z+-+3+%29%2A%28+z+-+4+%29+=+0+
+z+=+3+
+z+=+4+
-----------
+2%5Ex+=+3+
+x%2Alog%282%29+=+log%283%29+
+x+=+log%283%29+%2F+log%282%29+
By my calculator:
+x+=+1.585+
and
+2%5Ex+=+4+
+x%2Alog%282%29+=+log%284%29+
+x+=+log%284%29+%2F+log%282%29+
+x+=+2+
--------------
The roots are +x+=+1.585+, +x+=+2+
check:
+2%5Ex+%2B+12%282%29%5E%28-x%29+=+7+
+2%5E1.585+%2B+12%282%29%5E-1.585+=+7+
+3.00008+%2B+12%2A.33332+=+7+
+3+%2B+4+=+7+
OK
and, also
+2%5E2+%2B+12%282%29%5E-2+=+7+
+4+%2B+12%2A%281%2F4%29+=+7+
+4+%2B+3+=+7+
OK