SOLUTION: If log(base 3)2 = x simplify each logarithm a) log(base 3)8 b) log(base 3)24 c) log(base 3)√2 d) log(base 3)6√2 Can you please help me out? Thanks so much in a

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If log(base 3)2 = x simplify each logarithm a) log(base 3)8 b) log(base 3)24 c) log(base 3)√2 d) log(base 3)6√2 Can you please help me out? Thanks so much in a      Log On


   



Question 744927: If log(base 3)2 = x simplify each logarithm
a) log(base 3)8
b) log(base 3)24
c) log(base 3)√2
d) log(base 3)6√2

Can you please help me out? Thanks so much in advance:)
Can you also show all the steps because it would help me understand :)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How well do you understand what logs are?
If I say +a%5Eb+=+c+, then
+a+%7D%7D+is+the+base%0D%0A%7B%7B%7B+b+ is the log
+c+ is the result
So I can rewrite this exactly as:
+log%28+a%2Cc+%29+=+b+
----------------
The general rules are:
+log%28+a%2Ca+%29+=+1+
+log%28+a+%29+%2B+log%28+b+%29+=+log%28+a%2Ab+%29 ( the base can be 10, or anything else )
+log%28+a%5E2+%29+=+2%2Alog%28a%29+ ( again, the base can be anything )
----------------
+log%28+3%2C2+%29+=+x+
a)
+log%28+3%2C8+%29+=+log%28+3%2C+2%5E3+%29+
+log%28+3%2C+2%5E3+%29+=+3%2Alog%28+3%2C2+%29+
+3%2Alog%28+3%2C2+%29+=+3x+
b)
+log%28+3%2C24+%29+=+log%28+3%2C+3%2A8+%29+
+log%28+3%2C+3%2A8+%29+=+log%28+3%2C3+%29+%2B+log%28+3%2C8+%29+
++log%28+3%2C3+%29+%2B+log%28+3%2C8+%29+=+1+%2B+3x+
c)
+log%28+3%2C+sqrt%282%29%29+=+log%28+3%2C+2%5E%281%2F2%29%29+
++log%28+3%2C+2%5E%281%2F2%29%29+=+%281%2F2%29%2Alog%28+3%2C+2+%29+
+%281%2F2%29%2Alog%28+3%2C+2+%29+=+x%2F2+
d)
+log%28+3%2C+6%2Asqrt%282%29+%29+=+log%28+3%2C6+%29+%2B+log%28+3%2C+sqrt%282%29+%29+



+x+%2B+1+%2B+x%2F2+=+1+%2B+%283x%29%2F2+