Solve ((3)^(x+1)-1)/(2)=(120)/(1) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ { 3 }^{ x+1 } -1 }{ 2 } = \frac{ 120 }{ 1 }$$

Solve for x

$x=\log_{3}\left(241\right)-1\approx 3.992477319$

Steps Using Definition of Logarithm

Multiply both sides of the equation by $2$.

$$3^{x+1}-1=2\times 120$$

Multiply $2$ and $120$ to get $240$.

$$3^{x+1}-1=240$$

Add $1$ to both sides of the equation.

$$3^{x+1}=241$$

Take the logarithm of both sides of the equation.

$$\log(3^{x+1})=\log(241)$$

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

$$\left(x+1\right)\log(3)=\log(241)$$

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

$$x+1=\frac{\log(241)}{\log(3)}$$

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

$$x+1=\log_{3}\left(241\right)$$

Subtract $1$ from both sides of the equation.

$$x=\log_{3}\left(241\right)-1$$

Solve for x (complex solution)

$x=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(241\right)-1$
$n_{1}\in \mathrm{Z}$