Precalculus Examples

$4.6 = \log (\frac{x}{y}) \cdot 794$

Step 1

Rewrite the equation as $\log (\frac{x}{y}) \cdot 794 = 4.6$ .

$\log (\frac{x}{y}) \cdot 794 = 4.6$

Step 2

Divide each term in $\log (\frac{x}{y}) \cdot 794 = 4.6$ by $794$ and simplify.

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Step 2.1

Divide each term in $\log (\frac{x}{y}) \cdot 794 = 4.6$ by $794$ .

$\frac{\log (\frac{x}{y}) \cdot 794}{794} = \frac{4.6}{794}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $794$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{\log (\frac{x}{y}) \cdot 794}{794} = \frac{4.6}{794}$

Step 2.2.1.2

Divide $\log (\frac{x}{y})$ by $1$ .

$\log (\frac{x}{y}) = \frac{4.6}{794}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $4.6$ by $794$ .

$\log (\frac{x}{y}) = 0.00579345$

Step 3

Rewrite $\log (\frac{x}{y}) = 0.00579345$ 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 $b^{y} = x$ .

$10^{0.00579345} = \frac{x}{y}$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $\frac{x}{y} = 10^{0.00579345}$ .

$\frac{x}{y} = 10^{0.00579345}$

Step 4.2

Multiply both sides by $y$ .

$\frac{x}{y} y = 10^{0.00579345} y$

Step 4.3

Simplify.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Cancel the common factor of $y$ .

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Step 4.3.1.1.1

Cancel the common factor.

$\frac{x}{y} y = 10^{0.00579345} y$

Step 4.3.1.1.2

Rewrite the expression.

$x = 10^{0.00579345} y$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Raise $10$ to the power of $0.00579345$ .

$x = 1.01342928 y$