Answer:
To find : The error in the solution and what additional step needs to be completed?
Solution : The mistake is the step 3 and additional step need to be added after it.
Step 1 - \log x -\log_5 3 = 2\log_5 3logx−log
5
3=2log
5
3
Step 2 - \log x = 3\log_5 3logx=3log
5
3
Step 3 - \log x =\log_5 3^3logx=log
5
3
3
Step 4 - \log x=\log_5 27logx=log
5
27
Applying change base rule of logarithmic, \log_b a=\frac{\log a}{\log b}log
b
a=
logb
loga
Step 5 - \log x=\frac{\log 27}{\log 5}logx=
log5
log27
Step 6 - \log x=\frac{1.431}{0.698}logx=
0.698
1.431
Step 7 - \log x=2.050logx=2.050
Step 8 - x=10^{2.050}x=10
2.050
Step 9 - x=112.20x=112.20
From step 4 to 9 is the required steps.