Question

Paul and Scott are solving ${\log }_{3}x=9$.

Who is correct? Explain your reasoning.

Short answer

Scott is correct.

Step-by-step solution

Step 1. Given Information.

The solution for ${\log }_{3}x=9$by Paul and Scott is below.

And who among Paul and Scott is correct is to be determined.

Step 2. Explanation.

The function $a=b^c$ is an exponential function and the equivalent logarithmic form is given by $c={\log }_{b}a$.

In Paul solving the equation, in the second step ${\log }_{3}x$ is directly replaced by $3^x$ which is not possible.

And the Scott’s solution is correct.

Step 3. Conclusion.

Hence, Scott is correct.