SOLUTION: Please help with this. I can't understand the way my teacher is trying to explain. Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2 evaluate the following: 1. l

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help with this. I can't understand the way my teacher is trying to explain. Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2 evaluate the following: 1. l      Log On


   



Question 563670: Please help with this. I can't understand the way my teacher is trying to explain.
Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2
evaluate the following:
1. log (b)5/3
2. log (b)3b^2
3. log (b)45
4. log (b)(b/15)
Thank you so much for your help

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is just making use of general rules of logs:
(1) +log%28a%2Ab%29+=+log%28a%29+%2B+log%28b%29+
(2) +log%28a%2Fb%29+=+log%28a%29++-+log%28b%29+
(3) +log%28a%5Eb%29+=+b%2Alog%28a%29+
(4) +log%28b%2Cb%29+=+1+
All these rules can use any base for the logs
-------------------------------------
+log%28+b%2C3+%29+=+1.5+
+log%28+b%2C5+%29+=+2.2+
-----------------
(1)
+log%28+b%2C5%2F3+%29+=+log%28+b%2C5+%29+-+log%28+b%2C3+%29+
+log%28+b%2C5%2F3+%29+=+2.2+-+1.5+
+log%28+b%2C5%2F3+%29+=+.7+
-----------------
(2)
+log%28+b%2C3b%5E2+%29+=+log%28b%2C3%29+%2B+2%2Alog%28b%2Cb%29+
+log%28+b%2C3b%5E2+%29+=+1.5+%2B+2%2A1+
+log%28+b%2C3b%5E2+%29+=+3.5+
-----------------
(3)
+log%28+b%2C45+%29+=+log%28b%2C9%29+%2B+log%28b%2C5%29+
+log%28+b%2C45+%29+=+log%28b%2C3%5E2%29+%2B+2.2+
+log%28+b%2C45+%29+=+2%2Alog%28b%2C3%29+%2B+2.2+
+log%28+b%2C45+%29+=+2%2A1.5+%2B+2.2+
+log%28+b%2C45+%29+=+5.2+
-----------------
(4)
+log%28+b%2Cb%2F15+%29+=+log%28+b%2Cb+%29+-+log%28+b%2C15+%29+
+log%28+b%2Cb%2F15+%29+=+1+-+log%28+b%2C3%2A5+%29+
+log%28+b%2Cb%2F15+%29+=+1+-+log%28+b%2C3+%29+-+log%28+b%2C5+%29+
+log%28+b%2Cb%2F15+%29+=+1+-+1.5+-+2.2+
+log%28+b%2Cb%2F15+%29+=+1+-+3.7+
+log%28+b%2Cb%2F15+%29+=+-2.7+