Solve for x natural log of 21x+4 = natural log of 10

$\ln (21 x + 4) = \ln (10)$

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

$21 x + 4 = 10$

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$21 x = 10 - 4$

Subtract $4$ from $10$ .

$21 x = 6$

Divide each term in $21 x = 6$ by $21$ and simplify.

Divide each term in $21 x = 6$ by $21$ .

$\frac{21 x}{21} = \frac{6}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 x}{21} = \frac{6}{21}$

Divide $x$ by $1$ .

$x = \frac{6}{21}$

Simplify the right side.

Cancel the common factor of $6$ and $21$ .

Factor $3$ out of $6$ .

$x = \frac{3 (2)}{21}$

Cancel the common factors.

Factor $3$ out of $21$ .

$x = \frac{3 \cdot 2}{3 \cdot 7}$

Cancel the common factor.

$x = \frac{3 \cdot 2}{3 \cdot 7}$

Rewrite the expression.

$x = \frac{2}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{7}$

Decimal Form:

$x = 0.\overline{285714}$