Thursday, May 10th

[Lara Hulbert]

Throwback to Algebra 2:

Write the following expression under one logarithm and simplify.

[Cassandra Ruch]

Now that I'm back from the beach, I have time for some math (yay!).  I got 0 for the answer.

Basic logarithmic rules:

1. log(xy) = log(x) + log(y)

2. log(x/y) = log(x) - log(y)

3. log(x^y) = y log(x)

For the first section - log(a^2-10a+25):

1. a^2-10a+25 can be rewritten as (a-5)^2 so it looks like: log((a-5)^2)

For the middle section - 1/2 log(1/(a-5)^3):

1. Based on logarithmic rule #3, this can be rewritten as: log((1/(a-5)^3)^(1/2))

2. I then multiplied the exponent out, so it looks like: log(1/((a-5)^(3/2)))

 

For the last section - log(sqrt(a-5)):

1. This can be rewritten as log((a-5)^(1/2))

 

Putting it all together I got: log((a-5)^2) + log(1/((a-5)^(3/2))) - log((a-5)^(1/2))

 

Based on logarithmic rule #1, I combined the first and second terms by multiplying them:

 log((a-5)^2) + log(1/((a-5)^(3/2))) = log[((a-5)^2)/((a-5)^(3/2))]

This then simplifies to: log((a-5)^(1/2)) by subtracting the exponents.  

Now I'm left with: log((a-5)^(1/2)) - log((a-5)^(1/2))

Based on logarithmic rule #1, I combined these two terms by dividing them:

log((a-5)^(1/2)) - log((a-5)^(1/2)) = log[((a-5)^(1/2)/((a-5)^(1/2)) = log(1) = 0

--
You received this message because you are subscribed to the Google Groups "Math Problem of the Day" group.
To unsubscribe from this group and stop receiving emails from it, send an email to problem-of-the-...@googlegroups.com.
For more options, visit https://groups.google.com/groups/opt_out.