When a student solved the equation log x + 4 = 8, they arrived at the answer x = 99,999,996. Describe a possible reason for the error and give the correct solution.

Accepted Solution

Answer:[tex]x=10,000[/tex]Step-by-step explanation:The student has  considered [tex](x+4)[/tex] together, that looks a possible reason for the error because considering [tex]log(x+4) = 8[/tex] will give [tex](x+4) = 10^8\\x+4 = 100,000,000\\x= 99,999,996[/tex]Thus we say the [tex]logx[/tex] and [tex]4[/tex] are separate.Solving [tex]log x + 4 = 8[/tex],We need to isolate [tex]log x[/tex]Subtracting [tex]4[/tex] from both side[tex]log x + 4-4 = 8-4\\logx = 4[/tex]Taking anti-log both side gives,[tex]logx = 4\\x= 10^4\\x=10000[/tex]Thus [tex]x=10,000[/tex] is the appropriate answer.