SOLUTION: 1)Write as a single logarithm and simplify log(base 2)√5 - log(base 2)√45 Can you please help me out? Also can you please show me the steps it would really help

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1)Write as a single logarithm and simplify log(base 2)√5 - log(base 2)√45 Can you please help me out? Also can you please show me the steps it would really help       Log On


   

Question 747765: 1)Write as a single logarithm and simplify
log(base 2)√5 - log(base 2)√45
Can you please help me out?
Also can you please show me the steps it would really help me understand? Thanks so much in advance:)
Found 2 solutions by Alan3354, rothauserc:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1)Write as a single logarithm and simplify
log(base 2)√5 - log(base 2)√45
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log%282%2Csqrt%285%29%29+-+log%282%2Csqrt%2845%29%29
Subtracting logs --> division
That's the only step.
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I doubt I'm the only tutor who is tired of seeing "Also can you please show me the steps it would really help me understand? "
If you have questions about the solutions you can ask them.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We are asked to
1)Write as a single logarithm and simplify
log(base 2)√5 - log(base 2)√45
definition of logarithm
x = b^y, then y is the logarithm of x to base b
y = log(base b) (x)
1.) log (base 2) sqrt 5
y = 1/2 * log (base 2) 5
2.) log(base 2) sqrt(45)
y = 1/2 * log (base 2) 45 = 1/2 * (log (base 2) 5 + log (base 2) 9)
now we can write
1/2*log(base 2) 5 - 1/2*log(base 2) 5 - 1/2*log(base 2) 9
and we are left with
-1/2*log(base 2) 9 = -1/2 * 3 ( note 3^2 = 9)
= -3/2 = -1.5