SOLUTION: Evaluate each of the following. Don't just give a numerical answer; indicate clearly the log rules you used to calculate the answer? Suppose log a = 0.3, log b = -0.5. Evaluate

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Evaluate each of the following. Don't just give a numerical answer; indicate clearly the log rules you used to calculate the answer? Suppose log a = 0.3, log b = -0.5. Evaluate       Log On


   

Question 915828: Evaluate each of the following. Don't just give a numerical answer; indicate clearly the log rules you used to calculate the answer?
Suppose log a = 0.3, log b = -0.5. Evaluate each of the following. Don't just give a numerical answer; indicate clearly the log rules you used to calculate the answer

log(1000 a^2)
log(^4 root √(b/a))
that's a fourth root nested in the radical

Please explain how to solve.
Thank you
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate each of the following. Don't just give a numerical answer; indicate clearly the log rules you used to calculate the answer?
Suppose log a = 0.3, log b = -0.5. Evaluate each of the following. Don't just give a numerical answer; indicate clearly the log rules you used to calculate the answer

log(1000 a^2) = log(1000) + 2*log(a)
Rule: log(A*B) = log(A) + log(B)
Rule: log(A^n) = n*log(A)
---------------------------
Your Problem::
= 3 + 2*0.3
= 3.06
---------------------------------
log(4 root √(b/a))
= log(b/a)^(1/4)
= (1/4)(log(b) - log(a))
= (1/4)(-0.5-0.3) = (1/4)(-0.8) = -0/2
Rule:: log(A/B) = log(A) - log(B)
----
Cheers,
Stan H.
------------