Solve for I L=10 log of I/I_0

$L = 10 \log (\frac{I}{I_{0}})$

Step 1

Rewrite the equation as $10 \log (\frac{I}{I_{0}}) = L$ .

$10 \log (\frac{I}{I_{0}}) = L$

Step 2

Divide each term in $10 \log (\frac{I}{I_{0}}) = L$ by $10$ and simplify.

Divide each term in $10 \log (\frac{I}{I_{0}}) = L$ by $10$ .

$\frac{10 \log (\frac{I}{I_{0}})}{10} = \frac{L}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 \log (\frac{I}{I_{0}})}{10} = \frac{L}{10}$

Divide $\log (\frac{I}{I_{0}})$ by $1$ .

$\log (\frac{I}{I_{0}}) = \frac{L}{10}$

Step 3

Rewrite $\log (\frac{I}{I_{0}}) = \frac{L}{10}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{\frac{L}{10}} = \frac{I}{I_{0}}$

Step 4

Solve for $I$ .

Rewrite the equation as $\frac{I}{I_{0}} = 10^{\frac{L}{10}}$ .

$\frac{I}{I_{0}} = 10^{\frac{L}{10}}$

Multiply both sides by $I_{0}$ .

$\frac{I}{I_{0}} I_{0} = 10^{\frac{L}{10}} I_{0}$

Simplify.

Simplify the left side.

Cancel the common factor of $I_{0}$ .

Cancel the common factor.

$\frac{I}{I_{0}} I_{0} = 10^{\frac{L}{10}} I_{0}$

Rewrite the expression.

$I = 10^{\frac{L}{10}} I_{0}$

Simplify the right side.

Reorder factors in $10^{\frac{L}{10}} I_{0}$ .

$I = I_{0} \cdot 10^{\frac{L}{10}}$

Solve for I L=10 log of I/I_0

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