SOLUTION: Please explain the method you would use, lo step by step, to solve this problem, if x=log 2 and y= log 3, express log36/log4 in terms of x and y

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please explain the method you would use, lo step by step, to solve this problem, if x=log 2 and y= log 3, express log36/log4 in terms of x and y      Log On


   



Question 954207: Please explain the method you would use, lo step by step,
to solve this problem, if x=log 2 and y= log 3, express log36/log4 in terms of x and y

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%2836%29+%2F+log%284%29+
+log%28%284%2A9%29%29+%2F+log%284%29+
----------------------
Use the rule:
+log%28%28+a%2Ab+%29%29+=+log%28a%29+%2B+log%28b%29+
----------------------------
+%28+log%284%29+%2B+log%289%29+%29+%2F+log%284%29+
----------------------------
Use the rule:
+log%28%28+a%5Eb+%29%29+=+b%2Alog%28a%29+
+%28+log%28%28+2%5E2+%29%29+%2B+log%28%28+3%5E2+%29%29%29+%2F+log%28%28+2%5E2+%29%29+
+%28+2%2Alog%282%29+%2B+2%2Alog%283%29+%29+%2F+%28+2%2Alog%282%29+%29+
Divide top and bottom by 2
+%28+log%282%29+%2B+log%283%29+%29+%2F+log%282%29+
+x+=+log%282%29+
+y+=+log%283%29+
Substituting:
+%28+x+%2B+y+%29+%2F+x+
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check answer:
By my calculator:
+log%2836%29+=+1.5563+
+log%284%29+=+.60206+
+log%2836%29+%2F+log%284%29+=+1.5563+%2F+.60206+
++log%2836%29+%2F+log%284%29+=+2.5850+
and
+%28+log%282%29+%2B+log%283%29+%29+%2F+log%282%29+=+%28+.30103+%2B+.47712+%29+%2F+.30103+
+%28+log%282%29+%2B+log%283%29+%29+%2F+log%282%29+=+.77815+%2F+.30103+
+%28+log%282%29+%2B+log%283%29+%29+%2F+log%282%29+=+2.5850+
OK