SOLUTION: Hi I'm stuck on the following problem, would you help me out, please? Let log_b (3) = A and log_b(2) = C. log_b(sqrt(3/128)) I know the numerator will be 3^1/2 which is 1/2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi I'm stuck on the following problem, would you help me out, please? Let log_b (3) = A and log_b(2) = C. log_b(sqrt(3/128)) I know the numerator will be 3^1/2 which is 1/2      Log On


   

Question 926231: Hi I'm stuck on the following problem, would you help me out, please?
Let log_b (3) = A and log_b(2) = C.
log_b(sqrt(3/128))
I know the numerator will be 3^1/2 which is 1/2A, but unsure of what to do with sqrt(128) which equals 2^7.
Thank you!
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+b%2C3+%29+=+A+
+log%28+b%2C2+%29+=+C+
-------------------
+log%28+b%2C+2%5E7+%29+=+7%2Alog%28+b%2C+2+%29+
and
+7%2Alog%28+b%2C+2+%29+=+7C+
---------------------
+log%28+b%2C+%28+3%2F128+%29%5E%281%2F2%29+%29+=+%281%2F2%29%2Alog%28+b%2C+3%2F128+%29+


+A%2F2+-+%287%2F2%29%2AC+

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe this might be your answer.

logb(sqrt(128) equals:

logb(128^(1/2) which equals:

1/2 * logb(128) which equals:

1/2 * logb(2*64) which equals:

1/2 * (logb(2) + logb(64) which equals:

1/2 * logb(2) + 1/2 * logb(64) which equals:

1/2 * logb(2) + 1/2 * logb(8^2) which equals:

1/2 * logb(2) + 1/2 * 2 * logb(8) which equals:

1/2 * logb(2) + 1/2 * 2 * logb(2^3) which equals:

1/2 * logb(2) + 1/2 * 2 * 3 * logb(2) which can be simplified to:

1/2 * logb(2) + 3 * logb(2).

since logb(2) = C, this can be further simplified to:

1/2 * C + 3 * C which can then be combined into:

3.5 * C