SOLUTION: Use natural logarithms to solve the equation 8*2^z=18*12^z for z (three decimal places).

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Question 492964: Use natural logarithms to solve the equation 8*2^z=18*12^z for z (three decimal places).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It can be simplified first
+8%2A2%5Ez+=+18%2A12%5Ez+
Divide both sides by 2
+4%2A2%5Ez+=+9%2A12%5Ez+
+%282%5Ez%29+%2F+%2812%5Ez%29+=+9%2F4+%7D%7D%0D%0A%7B%7B%7B+%282%2F12%29%5Ez+=+9%2F4+
+%281%2F6%29%5Ez+=+%283%2F2%29%5E2+
Take the natural log of both sides
+z%2Aln%281%2F6%29+=+2%2Aln%283%2F2%29+
+z+=+2%2A%28%28ln%283%2F2%29%29+%2F+ln%281%2F6%29%29+
+z+=+2%2A%28.405465+%2F+-1.79176%29+
+z+=+-.452589+
+z+=+-.453+
check answer:
+8%2A2%5E%28-.453%29+=+8%2A.7305+
+5.844+
and
+18%2A12%5E%28-.453%29+=+5.839+
I think this is close enough