SOLUTION: Let x=log225 and y=log256. We have to write an algebraic expression for x and y. a)log2 b)log3 c)log5

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Let x=log225 and y=log256. We have to write an algebraic expression for x and y. a)log2 b)log3 c)log5      Log On


   

Question 1055273: Let x=log225 and y=log256. We have to write an algebraic expression for x and y.
a)log2
b)log3
c)log5
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x=log196 y=log225 z=log256
Express the following in terms of x, y, and/or z
1. Log2
256 = 2^8
log(2) = z/8
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2. Log3
log(9) = log(900) - log(100) = log(900) - 2
900 = 225*4
log(900) = y + z/4
log(9) = y + z/4 - 2
log%283%29+=+y%2F2+%2B+z%2F8+-+1
--------
3. Log5
log%285%29+=+log%2810%29+-+log%282%29+=+1+-+z%2F8
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4. Log7
196 = 2^2*7^2
log(196) = 2log(2) + 2log(7)
x = z/4 + 2log(7)
log%287%29+=+%28x+-+z%2F4%29%2F2+=+x%2F2+-+z%2F8
--------
5. Log10
log(10) = 1