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 error in Step 5, when simplify exponent of 53.

Explanation:

We need to choose error from step work

Step 1: Given

`\log x-\log 53 = 2\log 53`

Step 2: Add log 53 both sides

`\log x-\log 53 +\log 53= \log 53+2\log 53`

Step 3: Simplify (Combine the like term right side)

`\log x= 3\log 53`

Step 4: Using property of log

`\log x = \log 53^3`

Step 5: Eliminate log

`x = 53^3`

Step 6: Simplify the exponent

`x=148877`

Hence, The error in Step 5, when simplify exponent of 53.