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If log(x²−21)=2, then the value x will be
a. 13
b. -17
c. -11
d. 12

User Delrog
by
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1 Answer

4 votes

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.

User Shamim Ahmmed
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