$$ \left. \begin{array} { l } { 3 = 10 \log \frac { I _ { 1 } } { I _ { 0 } } } \ { \frac { I } { I _ { 0 } } = ? } \end{array} ight. $$

Question

$$ \left. \begin{array} { l } { 3 = 10 \log \frac { I _ { 1 } } { I _ { 0 } } } \ { \frac { I } { I _ { 0 } } = ? } \end{array} ight. $$

UpStudy AI · Accepted Answer

1. Start with the given equation:
   $$
   3 = 10 \log \frac{I_1}{I_0}
   $$

2. Divide both sides by 10 to isolate the logarithm:
   $$
   \frac{3}{10} = \log \frac{I_1}{I_0}
   $$

3. Rewrite the logarithmic equation in its exponential form:
   $$
   \frac{I_1}{I_0} = 10^{\frac{3}{10}}
   $$

4. Recognize that the second line asks for $$\frac{I}{I_0}$$. If we assume $$I = I_1$$, then:
   $$
   \frac{I}{I_0} = 10^{\frac{3}{10}}
   $$

5. Optionally, approximate the value:
   $$
   10^{\frac{3}{10}} \approx 10^{0.3} \approx 1.995 \, (\text{approximately } 2)
   $$

Thus, the final answer is:
$$
\frac{I}{I_0} = 10^{\frac{3}{10}}
$$
$$ \frac{I}{I_0} = 10^{0.3} $$

\( \left. \begin{array} { l } { 3 = 10 \log \frac { I _ { 1 } } { I _ { 0 } } } \\ { \frac { I } { I _ { 0 } } = ? } \end{array} \right. \)