Question

What is the error in the proof? The error is in step 3. The reason should be the quotient property of exponents. The error is in step 3. You cannot use a property of logarithms to prove that same property. The error is in step 2. The reason should be the quotient property of exponents. The error is in step 5. The student did not convert from exponential to logarithmic form correctly when solving for x and y.

Answer 1

Answer:

The error is in step 3. You cannot use a property of logarithms to prove that same property.

Step-by-step explanation:

Here we  the proof of the quotient rule as

If Logₐx = M and Logₐy = N

Then x = $a^M$ and y = $a^N$

x ÷ y = $a^M$ ÷  $a^N$ = $a^{(M-N)}$

Take log of both sides we get

Logₐ(x÷y) = Logₐ$a^{(M-N)}$

Logₐ(x÷y) =M-N logₐa

Logₐ(x÷y) =M-N

∴Logₐ(x÷y) = Logₐx - Logₐy