Algebra Examples

$6.5 = \log (\frac{I}{I_{0}})$

Step 1

Rewrite the equation as $\log (\frac{I}{I_{0}}) = 6.5$ .

$\log (\frac{I}{I_{0}}) = 6.5$

Step 2

Rewrite $\log (\frac{I}{I_{0}}) = 6.5$ 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 $b^{y} = x$ .

$10^{6.5} = \frac{I}{I_{0}}$

Step 3

Solve for $I$ .

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Step 3.1

Rewrite the equation as $\frac{I}{I_{0}} = 10^{6.5}$ .

$\frac{I}{I_{0}} = 10^{6.5}$

Step 3.2

Multiply both sides by $I_{0}$ .

$\frac{I}{I_{0}} I_{0} = 10^{6.5} I_{0}$

Step 3.3

Simplify.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

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

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Step 3.3.1.1.1

Cancel the common factor.

$\frac{I}{I_{0}} I_{0} = 10^{6.5} I_{0}$

Step 3.3.1.1.2

Rewrite the expression.

$I = 10^{6.5} I_{0}$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Raise $10$ to the power of $6.5$ .

$I = 3162277.66016838 I_{0}$