SOLUTION: I am having trouble with this work. I need to express this in expanded form (if possible) and write out each step. This is not for a test or quiz, just a problem and I appreciate

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am having trouble with this work. I need to express this in expanded form (if possible) and write out each step. This is not for a test or quiz, just a problem and I appreciate      Log On


   

Question 1092729: I am having trouble with this work. I need to express this in expanded form (if possible) and write out each step. This is not for a test or quiz, just a problem and I appreciate if someone would show me all the steps. Thank you very much.
log(base "b") x^3 (times) sqrt(y)
In English: log(base "b") then the letter "x" to the power of three, then all of that times the square root of y
Thanks.
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(log(b) x^3) * y^(1/2) =
:
(3 * log(b) x) * y^(1/2) =
:
3 * log(b) (x) * y^(1/2)
:
in English
:
three times log base b of x times square root of y

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
log%28b%2C%28x%5E3%2Asqrt%28y%29%29%29 = log%28b%2C%28x%5E3%29%29 + log%28b%2C%28sqrt%28y%29%29%29 = 3%2Alog%28b%2C%28x%29%29 + %281%2F2%29%2Alog%28b%2C%28y%29%29.

Both x and y are assumed non-negative numbers.


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Now on "how to write it".

log(b, (x^3*sqrt(y))


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On logarithms and their properties, see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".