Precalculus Examples

$\log_{5} (3 x) = \log_{5} (2 + 4 x)$

Step 1

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

$3 x = 2 + 4 x$

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

Subtract $4 x$ from both sides of the equation.

$3 x - 4 x = 2$

Step 2.1.2

Subtract $4 x$ from $3 x$ .

$- x = 2$

Step 2.2

Divide each term in $- x = 2$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- x = 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{2}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{2}{- 1}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x = \frac{2}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $2$ by $- 1$ .

$x = - 2$

Step 3

Exclude the solutions that do not make $\log_{5} (3 x) = \log_{5} (2 + 4 x)$ true.

$No solution$