To determine the value of x for the equation log$_{10}$(x + 1) = 2, the definition of logarithms is applied. Step 1: Apply the logarithm definition The expression log$_{10}$(x + 1) = 2 indicates that 10 to the power of 2 is equivalent to x + 1: \[ x + 1 = 10^2 \] Step 2: Solve for x Calculate $10^2$: \[ x + 1 = 100 \] Subtract 1 from both sides: \[ x = 100 - 1 \] \[ x = 99 \] Step 3: Verify the solution Substitute x = 99 into the original equation: \[ \log_{10}(99 + 1) = \log_{10}(100) \] As $100 = 10^2$, this simplifies to: \[ \log_{10}(100) = 2 \] The equation is satisfied. Step 4: Compare with options The calculated value of x is 99. Evaluating the options: - (a) 99: Matches the calculated value. - (b) 100: Substituting 100 yields log$_{10}$(100 + 1) = log$_{10}$(101), which is not equal to 2. - (c) 101: Substituting 101 yields log$_{10}$(101 + 1) = log$_{10}$(102), which is not equal to 2. - (d) 99.9: Substituting 99.9 yields log$_{10}$(99.9 + 1) = log$_{10}$(100.9), which is not equal to 2. Step 5: Conclusion The determined value of x is 99, confirming that option (a) 99 is the correct answer.