How to solve (3)^(x+1)-3=54

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (3)^(x+1)-3=54 | Equatix

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Question

$${ 3 }^{ x+1 } -3=54$$

Solve for x

$x=\log_{3}\left(19\right)\approx 2.680143859$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$3^{x+1}-3=54$$

Add $3$ to both sides of the equation.

$$3^{x+1}=57$$

Take the logarithm of both sides of the equation.

$$\log(3^{x+1})=\log(57)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$\left(x+1\right)\log(3)=\log(57)$$

Divide both sides by $\log(3)$.

$$x+1=\frac{\log(57)}{\log(3)}$$

By the change-of-base formula $\frac{\log(a)}{\log(b)}=\log_{b}\left(a\right)$.

$$x+1=\log_{3}\left(57\right)$$

Subtract $1$ from both sides of the equation.

$$x=\log_{3}\left(57\right)-1$$

Show Solution

Solve for x (complex solution)

$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(19\right)$
$n_{1}\in \mathrm{Z}$