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.

Step-by-step explanation:

The student has  considered together, that looks a possible reason for the error because considering will give

Thus we say the and are separate.

Solving ,

We need to isolate

Subtracting from both side

Taking anti-log both side gives,

Thus is the appropriate answer.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places