SOLUTION: use log of logarithm to expand expression log6(6x)

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Question 979485: use log of logarithm to expand expression log6(6x)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+6%2C+6x+%29+
I can say:
+y+=+log%28+6%2C+6x+%29+
The inverse of this is:
+6%5Ey+=+6x+
This is equivilant to:
+6%2A6%5E%28+y-1+%29+=+6x+
Divide both sides by +6+
+6%5E%28+y-1+%29+=+x+
The inverse is:
+y+-+1+=+log%28+6%2C+x+%29+
+y+=+log%28+6%2Cx+%29+%2B+1+
--------------------------
check:
Suppose +x+=+6%5E10+
+y+=+log%28+6%2C+%286x%29+%29+
+y+=+log%28+6%2C+%286%2A6%5E10%29+%29+
+y+=+log%28+6%2C+%286%5E11%29+%29+
+y+=+11+
and
+y+=+log%28+6%2Cx+%29+%2B+1+
+y+=+log%28+6%2C%286%5E10%29+%29+%2B+1+
+y+=+10+%2B+1+
+y+=+11+
OK