Finite Math Examples

$\ln (7 x + 5) = \ln (2 x - 5)$

Step 1

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

$7 x + 5 = 2 x - 5$

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

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

$7 x + 5 - 2 x = - 5$

Step 2.1.2

Subtract $2 x$ from $7 x$ .

$5 x + 5 = - 5$

Step 2.2

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

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Step 2.2.1

Subtract $5$ from both sides of the equation.

$5 x = - 5 - 5$

Step 2.2.2

Subtract $5$ from $- 5$ .

$5 x = - 10$

Step 2.3

Divide each term in $5 x = - 10$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 x = - 10$ by $5$ .

$\frac{5 x}{5} = \frac{- 10}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 10}{5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10}{5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 10$ by $5$ .

$x = - 2$

Step 3

Exclude the solutions that do not make $\ln (7 x + 5) = \ln (2 x - 5)$ true.

$No solution$