Question

Solve for \( x \): 
\( \log_{10}(x^2) = 2 \).

• A. 10
• B. 100
• C. \(\pm 10\)
• D. \(\pm 100\)

Hint:

For logarithmic equations involving squares, consider both positive and negative roots.

Answer 1

The Correct Option is C

Step 1: Rewrite the equation: \[ \log_{10}(x^2) = 2 \] \[ x^2 = 10^2 = 100 \] Step 2: Solve for \( x \): \[ x = \pm \sqrt{100} = \pm 10 \] Step 3: Verify:
\[ \log_{10}(10^2) = \log_{10}(100) = 2 \] \[ \log_{10}((-10)^2) = \log_{10}(100) = 2 \] Both solutions are valid. This matches option (3).