Trigonometry Examples

$\log (4 y - 5) = \log (2 y - 1)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$4 y - 5 = 2 y - 1$

Step 2

Solve for $y$ .

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Step 2.1

Move all terms containing $y$ to the left side of the equation.

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Step 2.1.1

Subtract $2 y$ from both sides of the equation.

$4 y - 5 - 2 y = - 1$

Step 2.1.2

Subtract $2 y$ from $4 y$ .

$2 y - 5 = - 1$

Step 2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.1

Add $5$ to both sides of the equation.

$2 y = - 1 + 5$

Step 2.2.2

Add $- 1$ and $5$ .

$2 y = 4$

Step 2.3

Divide each term in $2 y = 4$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 y = 4$ by $2$ .

$\frac{2 y}{2} = \frac{4}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{4}{2}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $4$ by $2$ .

$y = 2$