If log(x - a) = 2 then x is equal to which of the following?

Rationale

x is equal to a + 100.

To solve the equation log(x - a) = 2, we can exponentiate both sides to find x. This leads to the equation x - a = 10², or x = a + 100.

A (a + 20) YOUR ANSWER

Substituting this choice into the original equation gives log((a + 20) - a) = log(20). Since log(20) does not equal 2 (which is log(100)), this option is incorrect.

B (a + 100) CORRECT

This choice works perfectly, as substituting it back yields log((a + 100) - a) = log(100), confirming that log(100) equals 2. Thus, this is the correct answer.

C (100a) YOUR ANSWER

Plugging 100a into the original equation results in log(100a - a) = log(99a). Since log(99a) does not equal 2 (as it would require 99a to equal 100), this option is not valid.

D (10 ^ (a + 2)) YOUR ANSWER

Substituting this choice into the equation yields log(10^(a + 2) - a) = log(10^(a + 2) - a). However, simplifying does not equate to 2, as it involves the variable a in a way that does not satisfy the original equation.

E (a²) YOUR ANSWER

If we replace x with a² in the original equation, we get log(a² - a). This expression does not simplify to 2 unless specific values for a are chosen, making this option generally incorrect.

Conclusion

The correct solution to the equation log(x - a) = 2 is x = a + 100. Evaluating the choices reveals that only this option satisfies the logarithmic condition, while all other choices fail to meet the criteria set by the equation. Understanding the properties of logarithms enables us to derive and verify the correct answer efficiently.

If log(x - a) = 2 then x is equal to which of the following?

x is equal to a + 100.

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