Trigonometry Examples

$\log_{7} (2 x + 1) = \log_{7} (10 - x)$

Step 1

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

$2 x + 1 = 10 - x$

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

Add $x$ to both sides of the equation.

$2 x + 1 + x = 10$

Step 2.1.2

Add $2 x$ and $x$ .

$3 x + 1 = 10$

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 $1$ from both sides of the equation.

$3 x = 10 - 1$

Step 2.2.2

Subtract $1$ from $10$ .

$3 x = 9$

Step 2.3

Divide each term in $3 x = 9$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $9$ by $3$ .

$x = 3$