How to solve a ) 9 ^ x = 6561

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 a ) 9 ^ x = 6561 | Equatix

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$$9 ^ { x } = 6561$$

$x=4$

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

$$9^{x}=6561$$

Take the logarithm of both sides of the equation.

$$\log(9^{x})=\log(6561)$$

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

$$x\log(9)=\log(6561)$$

Divide both sides by $\log(9)$.

$$x=\frac{\log(6561)}{\log(9)}$$

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

$$x=\log_{9}\left(6561\right)$$

$x=\frac{\pi n_{1}i}{\ln(3)}+4$
$n_{1}\in \mathrm{Z}$