Question

Explain the error in the solution below. What additional step needs to be completed? log x – log53 = 2log53 log x = 3log53 log x = log533 x = 27

Answer 1

The bases of the logarithms are not the same.The one-to-one property does not apply when the bases are not the same.The change of base formula should have been used to write the logarithms with the same base. 
I just checked it on Edge

Answer 2

Answer:

Error is in the step 3,

From step 4 to 9 is the required steps.

Step-by-step explanation:

Given : Solution below,

$\log x -\log_5 3 = 2\log_5 3\\\log x = 3\log_5 3\\\log x = \log_5 33\\x = 27$

To find : The error in the solution and what additional step needs to be completed?

Solution : The mistake is in the step 3 and additional step need to be added after it.

So we proceed it by starting,

Step 1 - $\log x -\log_5 3 = 2\log_5 3$

Step 2 - $\log x = 3\log_5 3$

Step 3 - $\log x =\log_5 3^3$

Step 4 - $\log x=\log_5 27$

Applying change base rule of logarithmic,

$\log_b a=\frac{\log a}{\log b}$

Step 5 - $\log x=\frac{\log 27}{\log 5}$

Step 6 - $\log x=\frac{1.431}{0.698}$

Step 7 - $\log x=2.050$

Step 8 - $x=10^{2.050}$

Step 9 - $x=112.20$

From step 4 to 9 is the required steps.