Question

A student solved log4(2x – 12) = 3, as shown.
Step 1: 2x – 12 = 34
Step 2: 2x – 12 = 81
Step 4: 2x = 93
Step 5: x = 46.5
Explain the error and find the correct solution.
(you will not receive "Brainliest" if answer isnt FULLY explained or correct. i will report absurd answer every time.

Answer 1

1-When you have a the logarithm given in the problem above, you can solve it by using the correct properties for logaritms.
 2- The students could solve it as below:
 log4(2x-12)=3
 4^[ log4(2x-12)]=4^3
 3- By definition a^log(x)=x, therefore,
 2x-12=4^3
 2x-12=64
 4- Now, the students can solve for x:
 x=38
  The first step is incorrect, because the term on the right member must be 4^3.

Answer 2

Answer:

The correct answer is x = 38.

Step-by-step explanation:

The error is in Step 1. They translated from logarithmic to exponential form incorrectly.

The student should have used 4 as the base and 3 as the exponent. This would result in 64, not 81, on the right side of the equation.