Solve for x 5 natural log of 4x-6=-6

$5 \ln (4 x - 6) = - 6$

Divide each term by $5$ and simplify.

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Divide each term in $5 \ln (4 x - 6) = - 6$ by $5$ .

$\frac{5 \ln (4 x - 6)}{5} = \frac{- 6}{5}$

Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 \ln (4 x - 6)}{5} = \frac{- 6}{5}$

Divide $\ln (4 x - 6)$ by $1$ .

$\ln (4 x - 6) = \frac{- 6}{5}$

Move the negative in front of the fraction.

$\ln (4 x - 6) = - \frac{6}{5}$

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

$e^{\ln (4 x - 6)} = e^{- \frac{6}{5}}$

Solve for $x$

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Simplify the equation.

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Exponentiation and log are inverse functions.

$4 x - 6 = e^{- \frac{6}{5}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 x - 6 = \frac{1}{e^{\frac{6}{5}}}$

Add $6$ to both sides of the equation.

$4 x = \frac{1}{e^{\frac{6}{5}}} + 6$

Divide each term by $4$ and simplify.

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Divide each term in $4 x = \frac{1}{e^{\frac{6}{5}}} + 6$ by $4$ .

$\frac{4 x}{4} = \frac{1}{e^{\frac{6}{5}}} \cdot \frac{1}{4} + \frac{6}{4}$

Cancel the common factor of $4$ .

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Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{e^{\frac{6}{5}}} \cdot \frac{1}{4} + \frac{6}{4}$

Divide $x$ by $1$ .

$x = \frac{1}{e^{\frac{6}{5}}} \cdot \frac{1}{4} + \frac{6}{4}$

Simplify each term.

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Multiply $\frac{1}{e^{\frac{6}{5}}}$ and $\frac{1}{4}$ .

$x = \frac{1}{e^{\frac{6}{5}} \cdot 4} + \frac{6}{4}$

Move $4$ to the left of $e^{\frac{6}{5}}$ .

$x = \frac{1}{4 \cdot e^{\frac{6}{5}}} + \frac{6}{4}$

Cancel the common factor of $6$ and $4$ .

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Factor $2$ out of $6$ .

$x = \frac{1}{4 e^{\frac{6}{5}}} + \frac{2 (3)}{4}$

Cancel the common factors.

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Factor $2$ out of $4$ .

$x = \frac{1}{4 e^{\frac{6}{5}}} + \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{1}{4 e^{\frac{6}{5}}} + \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{4 e^{\frac{6}{5}}} + \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4 e^{\frac{6}{5}}} + \frac{3}{2}$

Decimal Form:

$x = 1.57529855 \dots$

Solve for x 5 natural log of 4x-6=-6

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