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

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


   

Question 172751: Please help me!
3. Simplify the following expressions:
a. X4 * X5
b. Z9/Z10
c. log3Y + log3Z
d. log5Y - log5Z
Answer by monika_p(71) About Me  (Show Source):
You can put this solution on YOUR website!
a.X%5E4+%2A+X%5E5+=+X%5E%284%2B5%29=x%5E9 use multiplication property of exponents with same base x%5Ea%2Ax%5Eb=x%5E%28a%2Bb%29
b. Z%5E9%2FZ%5E10+=z%5E%289-10%29=z%5E%28-1%29=1%2Fz use division property of exponents with same base x%5Ea%2Fx%5Eb=x%5E%28a-b%29 and reciprocal property x%5E%28-a%29=1%2Fx%5Ea
c. log3Y + log3Z= log3(Y*Z) use The Product Rule for Logarithms logxA+logxB=logx(A*B)

d. log5Y - log5Z=log5(Y/Z) use The Quotient Rule for Logarithms logxA-logxB=logx(A/b)