Question

Use the properties of logarithms to expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

a) log(x)+ 9/2 log(y)− 12/2log( √2)
b) 9/2 log(x)− 12/2log( √y)− 1/2log(2)
c) Both a and b
d) none of the above

Answer 1

To expand the given expression using the properties of logarithms, we can apply the rules of logarithms and rewrite the expression as a sum, difference, or product of logs.

Step-by-step explanation:

To expand the given expression using the properties of logarithms, we can apply the rules of logarithms:

a) log(x)+ 9/2 log(y)− 12/2log( √2) = log(x) + log(y^(9/2)) - log(√2^(12/2))

= log(x) + log(y^9) - log(2^6)

= log(x) + 9log(y) - 6log(2)

b) 9/2 log(x)− 12/2log( √y)− 1/2log(2) = log(x^(9/2)) - log(√y^(12/2)) - log(√2)

= log(x^9) - log(y^6) - log(√2)