Solve for x 2(3)^(x+1)=36

$2 {(3)}^{x + 1} = 36$

Divide each term in $(2 \cdot 3^{x + 1}) = 36$ by $2$ and simplify.

Divide each term in $(2 \cdot 3^{x + 1}) = 36$ by $2$ .

$\frac{(2 \cdot 3^{x + 1})}{2} = \frac{36}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 3^{x + 1}}{2} = \frac{36}{2}$

Divide $3^{x + 1}$ by $1$ .

$3^{x + 1} = \frac{36}{2}$

Simplify the right side.

Divide $36$ by $2$ .

$3^{x + 1} = 18$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (3^{x + 1}) = \ln (18)$

Expand $\ln (3^{x + 1})$ by moving $x + 1$ outside the logarithm.

$(x + 1) \ln (3) = \ln (18)$

Simplify the left side.

Simplify $(x + 1) \ln (3)$ .

Apply the distributive property.

$x \ln (3) + 1 \ln (3) = \ln (18)$

Multiply $\ln (3)$ by $1$ .

$x \ln (3) + \ln (3) = \ln (18)$

Move all the terms containing a logarithm to the left side of the equation.

$x \ln (3) + \ln (3) - \ln (18) = 0$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$x \ln (3) + \ln (\frac{3}{18}) = 0$

Cancel the common factor of $3$ and $18$ .

Factor $3$ out of $3$ .

$x \ln (3) + \ln (\frac{3 (1)}{18}) = 0$

Cancel the common factors.

Factor $3$ out of $18$ .

$x \ln (3) + \ln (\frac{3 \cdot 1}{3 \cdot 6}) = 0$

Cancel the common factor.

$x \ln (3) + \ln (\frac{3 \cdot 1}{3 \cdot 6}) = 0$

Rewrite the expression.

$x \ln (3) + \ln (\frac{1}{6}) = 0$

Subtract $\ln (\frac{1}{6})$ from both sides of the equation.

$x \ln (3) = - \ln (\frac{1}{6})$

Divide each term in $x \ln (3) = - \ln (\frac{1}{6})$ by $\ln (3)$ and simplify.

Divide each term in $x \ln (3) = - \ln (\frac{1}{6})$ by $\ln (3)$ .

$\frac{x \ln (3)}{\ln (3)} = \frac{- \ln (\frac{1}{6})}{\ln (3)}$

Simplify the left side.

Cancel the common factor of $\ln (3)$ .

Cancel the common factor.

$\frac{x \ln (3)}{\ln (3)} = \frac{- \ln (\frac{1}{6})}{\ln (3)}$

Divide $x$ by $1$ .

$x = \frac{- \ln (\frac{1}{6})}{\ln (3)}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{\ln (\frac{1}{6})}{\ln (3)}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\ln (\frac{1}{6})}{\ln (3)}$

Decimal Form:

$x = 1.63092975 \dots$

Solve for x 2(3)^(x+1)=36

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