How to solve 4 ^ (2x) = 1/32

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 4 ^ (2x) = 1/32 | Equatix

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$$4^{2x}=\frac{1}{32}$$

$x = -\frac{5}{4} = -1\frac{1}{4} = -1.25$

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

$$4^{2x}=\frac{1}{32}$$

Take the logarithm of both sides of the equation.

$$\log(4^{2x})=\log(\frac{1}{32})$$

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

$$2x\log(4)=\log(\frac{1}{32})$$

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

$$2x=\frac{\log(\frac{1}{32})}{\log(4)}$$

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

$$2x=\log_{4}\left(\frac{1}{32}\right)$$

Divide both sides by $2$.

$$x=-\frac{\frac{5}{2}}{2}$$

$x=\frac{i\pi n_{1}}{2\ln(2)}-\frac{5}{4}$
$n_{1}\in \mathrm{Z}$