Final answer:
After converting the logarithmic equation to its exponential form and solving, the two possible solutions are 11 and -11. Given the options in the question, the correct answer is -11.
Step-by-step explanation:
The given equation is log(x²-21)=2. To solve for x, we need to convert the logarithmic equation to its exponential form. Remember, if logb(A) = C, then bC = A. Applying this to our equation with a base of 10, we have 102 = x² - 21.
Simplify the equation:
- 102 = 100
- 100 = x² - 21
- 100 + 21 = x²
- 121 = x²
Now, take the square root of both sides:
- √121 = √x²
- 11 = x or -11 = x
It is clear that the two possible solutions are 11 and -11. However, looking at the options given in the question, 11 is not listed, but -11 is an option. Therefore, the correct answer to the question If log(x²-21)=2, then the value x will be? is c. -11.