Solve 4 ) 27 ^ (x + 1) = 9 | 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

$$27 ^ { x + 1 } = 9$$

Solve for x

$x=-\frac{1}{3}\approx -0.333333333$

Steps Using Definition of Logarithm

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

$$27^{x+1}=9$$

Take the logarithm of both sides of the equation.

$$\log(27^{x+1})=\log(9)$$

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

$$\left(x+1\right)\log(27)=\log(9)$$

Divide both sides by $\log(27)$.

$$x+1=\frac{\log(9)}{\log(27)}$$

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

$$x+1=\log_{27}\left(9\right)$$

Subtract $1$ from both sides of the equation.

$$x=\frac{2}{3}-1$$

Solve for x (complex solution)

$x=\frac{i\times 2\pi n_{1}}{3\ln(3)}-\frac{1}{3}$
$n_{1}\in \mathrm{Z}$