Question 15

x is equal to a + 100

To solve for x in the equation log(x - a) = 2, we can rewrite it in exponential form, yielding x - a = 10^2. Therefore, x = a + 100.

A) a + 20

This option is incorrect because if we substitute x with a + 20, we would have log(20) = 2, which does not hold true since 10^2 equals 100, not 20.

B) a + 100

This option is correct. By rewriting the logarithmic equation log(x - a) = 2 in exponential form, we find that x - a = 100. Thus, x = a + 100 satisfies the equation.

C) 100a

This option is incorrect as substituting x with 100a would give log(100a - a) = log(99a), which does not equal 2. The exponential form would imply that 99a = 100, which is not a valid solution.

D) 10 ^ (a + 2)

This option is incorrect because substituting x with 10^(a + 2) results in log(10^(a + 2) - a) = 2. The expression simplifies to log(10^2) = 2, but does not yield a valid simplification to derive x in the context of the original equation.

E) a²

This option is incorrect. If we substitute x with a², we get log(a² - a) = 2. The expression would require a² - a to equal 100, which is not a valid transformation from the original log equation.

Conclusion

The correct answer, a + 100, directly results from rewriting the logarithmic equation into its exponential form, leading to the valid solution for x. All other options fail to satisfy the equation derived from the logarithmic expression, thereby confirming that only option B is the correct choice.