Finite Math Examples

$\log (250) + x \cdot \log (1.6) = \log (50)$

Step 1

Simplify the left side.

$\log (250) + x \log (1.6) = \log (50)$

Step 2

Move all the terms containing a logarithm to the left side of the equation.

$\log (250) + x \log (1.6) - \log (50) = 0$

Step 3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$x \log (1.6) + \log (\frac{250}{50}) = 0$

Step 4

Simplify each term.

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Step 4.1

Log base $10$ of $1.6$ is approximately $0.20411998$ .

$x \cdot 0.20411998 + \log (\frac{250}{50}) = 0$

Step 4.2

Move $0.20411998$ to the left of $x$ .

$0.20411998 \cdot x + \log (\frac{250}{50}) = 0$

Step 4.3

Divide $250$ by $50$ .

$0.20411998 x + \log (5) = 0$

Step 5

Subtract $\log (5)$ from both sides of the equation.

$0.20411998 x = - \log (5)$

Step 6

Divide each term in $0.20411998 x = - \log (5)$ by $0.20411998$ and simplify.

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Step 6.1

Divide each term in $0.20411998 x = - \log (5)$ by $0.20411998$ .

$\frac{0.20411998 x}{0.20411998} = \frac{- \log (5)}{0.20411998}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $0.20411998$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{0.20411998 x}{0.20411998} = \frac{- \log (5)}{0.20411998}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \log (5)}{0.20411998}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$x = - \frac{\log (5)}{0.20411998}$

Step 6.3.2

Log base $10$ of $5$ is approximately $0.69897$ .

$x = - \frac{0.69897}{0.20411998}$

Step 6.3.3

Divide $0.69897$ by $0.20411998$ .

$x = - 1 \cdot 3.42430954$

Step 6.3.4

Multiply $- 1$ by $3.42430954$ .

$x = - 3.42430954$