How to solve (2 ^ 2) ^ x = 64

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 (2 ^ 2) ^ x = 64 | Equatix

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$$(2^{2})^{x}=64$$

$x=3$

Calculate $2$ to the power of $2$ and get $4$.

$$4^{x}=64$$

Take the logarithm of both sides of the equation.

$$\log(4^{x})=\log(64)$$

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

$$x\log(4)=\log(64)$$

Divide both sides by $\log(4)$.

$$x=\frac{\log(64)}{\log(4)}$$

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

$$x=\log_{4}\left(64\right)$$

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