Question

Use the Quotient Rule of Logarithms to write an expanded expression equivalent to log6 (2y-3/

y) Make sure to use parenthesis around your logarithm functions log(x + y).

Answer 1

To expand log6 (2y-3/y), we use the Quotient Rule of Logarithms which states that the logarithm of a quotient is the difference of the logarithms of the numerator and the denominator, resulting in log6 (2y-3) - log6 (y).

Step-by-step explanation:

To write an expanded expression equivalent to log6 (2y-3/y) using the Quotient Rule of Logarithms, we need to apply the rule that states the logarithm of a quotient is the difference between the logarithms of the numerator and the denominator.

The Quotient Rule of Logarithms tells us that:

loga (x/y) = loga x - loga y

Therefore, for log6 (2y-3/y), we split the logarithm into two parts:

log6 (2y-3) - log6 (y)

Note that parentheses are used around the logarithm functions when dealing with additions or subtractions to avoid confusion.