Question

If log$_{10}$(x + 1) = 2, what is the value of x?

• A. 99
• B. 100
• C. 101
• D. 99.9

Hint:

To solve log$_{10}$(a) = b, use a = $10^b$.
Always verify by substituting the value back into the original equation.

Answer 1

The Correct Option is A

To find the value of x given the equation log$_{10}$(x + 1) = 2, 
we use the definition of logarithms. 
Step 1: Apply the logarithm definition 
The equation log$_{10}$(x + 1) = 2 means that 10 raised to the power of 2 
equals x + 1: 
\[ x + 1 = 10^2 \] Step 2: Solve for x 
Calculate $10^2$: 
\[ x + 1 = 100 \] \[ x = 100 - 1 \] \[ x = 99 \] Step 3: Verify the solution 
Substitute x = 99 back into the original equation: 
\[ \log_{10}(99 + 1) = \log_{10}(100) \] Since $100 = 10^2$, 
\[ \log_{10}(100) = 2 \] The equation holds true. 
Step 4: Compare with options 
- (a) 99 matches the calculated value. 
- (b) 100 would give log$_{10}(100 + 1) = \log_{10}(101) \neq 2$. 
- (c) 101 would give log$_{10}(101 + 1) = \log_{10}(102) \neq 2$. 
- (d) 99.9 would give log$_{10}(99.9 + 1) = \log_{10}(100.9) \neq 2$. 
Step 5: Conclusion 
The value of x is 99, making (a) 99 the correct answer.