Solve for x 2 natural log of 8x+7-12=0

$2 \ln (8 x + 7) - 12 = 0$

Step 1

Add $12$ to both sides of the equation.

$2 \ln (8 x + 7) = 12$

Step 2

Divide each term in $2 \ln (8 x + 7) = 12$ by $2$ and simplify.

Divide each term in $2 \ln (8 x + 7) = 12$ by $2$ .

$\frac{2 \ln (8 x + 7)}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \ln (8 x + 7)}{2} = \frac{12}{2}$

Divide $\ln (8 x + 7)$ by $1$ .

$\ln (8 x + 7) = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$\ln (8 x + 7) = 6$

Step 3

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (8 x + 7)} = e^{6}$

Step 4

Rewrite $\ln (8 x + 7) = 6$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{6} = 8 x + 7$

Step 5

Solve for $x$ .

Rewrite the equation as $8 x + 7 = e^{6}$ .

$8 x + 7 = e^{6}$

Subtract $7$ from both sides of the equation.

$8 x = e^{6} - 7$

Divide each term in $8 x = e^{6} - 7$ by $8$ and simplify.

Divide each term in $8 x = e^{6} - 7$ by $8$ .

$\frac{8 x}{8} = \frac{e^{6}}{8} + \frac{- 7}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{e^{6}}{8} + \frac{- 7}{8}$

Divide $x$ by $1$ .

$x = \frac{e^{6}}{8} + \frac{- 7}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{e^{6}}{8} - \frac{7}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{e^{6}}{8} - \frac{7}{8}$

Decimal Form:

$x = 49.55359918 \dots$

Solve for x 2 natural log of 8x+7-12=0

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