Finite Math Examples

$x \log (2) = x - 1 \log (3)$

Step 1

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

$x \log (2) + 1 \log (3) = x$

Step 2

Multiply $\log (3)$ by $1$ .

$x \log (2) + \log (3) = x$

Step 3

Subtract $x$ from both sides of the equation.

$x \log (2) + \log (3) - x = 0$

Step 4

Subtract $\log (3)$ from both sides of the equation.

$x \log (2) - x = - \log (3)$

Step 5

Factor $x$ out of $x \log (2) - x$ .

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Step 5.1

Factor $x$ out of $x \log (2)$ .

$x (\log (2)) - x = - \log (3)$

Step 5.2

Factor $x$ out of $- x$ .

$x (\log (2)) + x \cdot - 1 = - \log (3)$

Step 5.3

Factor $x$ out of $x (\log (2)) + x \cdot - 1$ .

$x (\log (2) - 1) = - \log (3)$

Step 6

Divide each term in $x (\log (2) - 1) = - \log (3)$ by $\log (2) - 1$ and simplify.

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Step 6.1

Divide each term in $x (\log (2) - 1) = - \log (3)$ by $\log (2) - 1$ .

$\frac{x (\log (2) - 1)}{\log (2) - 1} = \frac{- \log (3)}{\log (2) - 1}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $\log (2) - 1$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{x (\log (2) - 1)}{\log (2) - 1} = \frac{- \log (3)}{\log (2) - 1}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \log (3)}{\log (2) - 1}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$x = - \frac{\log (3)}{\log (2) - 1}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\log (3)}{\log (2) - 1}$

Decimal Form:

$x = 0.68260619 \dots$