Assuming $log\left(x\right)$ denotes the common logarithm (base $10$), if $log\left(x\right)=-0.123$, what is the value of $x$?

• A. $x={10}^{0.123}$
• B. $x={0.123}^{10}$
• C. $x={10}^{-0.123}$
• D. $x=-{10}^{-0.123}$

Answer: (C)

Verified step by step guidance

1. Recall the definition of the common logarithm: if \(\log(x) = y\), then \(x = 10^y\) because the base of the common logarithm is 10.
2. Given the equation \(\log(x) = -0.123\), identify \(y = -0.123\) in the definition above.
3. Rewrite the equation in exponential form using the definition: \(x = 10^{-0.123}\).
4. Understand that this expression means \(x\) is 10 raised to the power of \(-0.123\), which is the inverse operation of taking the logarithm.
5. Note that the other options given either have the base and exponent reversed or incorrectly include a negative sign outside the exponentiation, which does not follow the logarithm-exponent relationship.