Question

If \(\log(10x)=3\), what is the value of \(x\)?

• A. \(10\)
• B. \(100\)
• C. \(1{,}000\)
• D. \(1\)

Hint:

To solve \(\log_{10}(A)=k\), rewrite as \(A=10^{k}\). Then isolate the unknown. Always verify by substituting back.

Answer 1

The Correct Option is B

Solution:
Step 1 (Interpret the logarithm).
Here \(\log\) denotes the common logarithm (base \(10\)). Given \(\log(10x)=3\).
Step 2 (Convert log form to exponential form).
\(\log_{10}(10x)=3 10x=10^{3}\).
Step 3 (Solve for \(x\)).
\(10x=1000 x=\dfrac{1000}{10}=100\).
Step 4 (Verification).
Check: \(\log(10\cdot 100)=\log(1000)=3\) (true).
\[ {100 \ \text{(Option (b)}} \]