SOLUTION: Please help me! 3. Simplify the following expressions: a. X4 * X5 b. Z9/Z10 c. log3Y + log3Z d. log5Y - log5Z

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me! 3. Simplify the following expressions: a. X4 * X5 b. Z9/Z10 c. log3Y + log3Z d. log5Y - log5Z      Log On

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Question 171516: Please help me!
3. Simplify the following expressions:
a. X4 * X5
b. Z9/Z10
c. log3Y + log3Z
d. log5Y - log5Z
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
I'll give you the rules and you can apply them yourself:

Rule 1: Multiplication of like variables

%28x%5Em%29%28x%5En%29=x%5E%28m%2Bn%29

This one makes sense if you consider x%2Ax=%28x%5E1%29%28x%5E1%29=x%5E%281%2B1%29=x%5E2

Rule 2: Division of like variables

%28x%5Em%29%2F%28x%5En%29=x%5E%28m-n%29

Rule 3: The sum of the logs is the log of the product

log%28b%2C%28x%5B1%5D%29%29%2Blog%28b%2C%28x%5B2%5D%29%29=log%28b%2C%28x%5B1%5Dx%5B2%5D%29%29

Rule 4: The difference of the logs is the log of the quotient

log%28b%2C%28x%5B1%5D%29%29-log%28b%2C%28x%5B2%5D%29%29=log%28b%2C%28x%5B1%5D%2Fx%5B2%5D%29%29