To prove the Quotient Rule of Logarithms, we need to write the quotient of m and n as m/n = b^x/b^y. This step is crucial in demonstrating how the logarithm of a quotient can be simplified to the difference of the logarithms of its individual components.
By writing m/n = b^x/b^y, we can then simplify this expression using the properties of exponents to show that log_b(m/n) = log_b(m) - log_b(n), which is the Quotient Rule of Logarithms.
Therefore, the correct option is to write the quotient of m and n as m/n = b^x/b^y.
You are proving the Quotient Rule of Logarithms. The following shows your work so far.
Let log b m = x and log b n = y .
log b m = x is equivalent to b^x = m .
log b n = y is equivalent to b^y=n .
Which of the following options best describes the next step you should take in this proof?
Responses
Write the difference between m and n as m−n = b^x − b^y. - incorrect
Write the sum of m and n as m+n= b^x + b^y. - incorrect
Write the quotient of m and n as m/n = b^x/b^y. - correct
Write the product of m and n as mn = b^x b^y. - incorrect
explain how you get the correct answer
1 answer
1 answer