SOLUTION: log 2 base 7 =m, then log 28 base 49 is equal to

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Question 980115: log 2 base 7 =m, then log 28 base 49 is equal to
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+2%2C7+%29+=+m+
The inverse is:
+2%5Em+=+7+
If I square both sides:
+2%5E%282m%29+=+49+
+7%5E2+=+2%5E%282m%29+
(1) +7%5E%28%282%2Fm%29%29+=+2%5E2+
---------------------
I will say:
+log%28+49%2C+28+%29+=+x+
the inverse is:
+49%5Ex+=+28+
This is the same as:
+7%5E%282x%29+=+28+
+7%5E%282x%29+=+7%2A4+
+7%5E%28+2x-1+%29+=+4+
(2) +7%5E%28+2x-1+%29+=+2%5E2+
------------------------
Comparing (1) and (2), I can say:
+7%5E%28+2x-1+%29+=+7%5E%282%2Fm%29+
+2x+-+1+=+2%2Fm+
+2x+=+2%2Fm+%2B+1+
+x+=+1%2Fm+%2B+1%2F2+ answer
check:
+2%5Em+=+7+
+m+=+.8451%2F.30103+
+m+=+2.80736+
--------------------
I said:
+x+=+1%2Fm+%2B+1%2F2+
+x+=+1%2F2.80736+%2B+1%2F2+
+x+=+.85621+
and
+49%5Ex+=+28+
+49%5E.85621+=+28+
+28.0003+=+28+
close enough