Basic Math Examples

$4 \log (3 - 2 y) = 1$

Step 1

Divide each term in $4 \log (3 - 2 y) = 1$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 \log (3 - 2 y) = 1$ by $4$ .

$\frac{4 \log (3 - 2 y)}{4} = \frac{1}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 \log (3 - 2 y)}{4} = \frac{1}{4}$

Step 1.2.1.2

Divide $\log (3 - 2 y)$ by $1$ .

$\log (3 - 2 y) = \frac{1}{4}$

Step 2

Rewrite $\log (3 - 2 y) = \frac{1}{4}$ 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 $b^{y} = x$ .

$10^{\frac{1}{4}} = 3 - 2 y$

Step 3

Solve for $y$ .

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Step 3.1

Rewrite the equation as $3 - 2 y = 10^{\frac{1}{4}}$ .

$3 - 2 y = 10^{\frac{1}{4}}$

Step 3.2

Subtract $3$ from both sides of the equation.

$- 2 y = 10^{\frac{1}{4}} - 3$

Step 3.3

Divide each term in $- 2 y = 10^{\frac{1}{4}} - 3$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 y = 10^{\frac{1}{4}} - 3$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{10^{\frac{1}{4}}}{- 2} + \frac{- 3}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{10^{\frac{1}{4}}}{- 2} + \frac{- 3}{- 2}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{10^{\frac{1}{4}}}{- 2} + \frac{- 3}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Simplify each term.

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Step 3.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{10^{\frac{1}{4}}}{2} + \frac{- 3}{- 2}$

Step 3.3.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{10^{\frac{1}{4}}}{2} + \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{10^{\frac{1}{4}}}{2} + \frac{3}{2}$

Decimal Form:

$y = 0.61086029 \dots$