How to solve (16)^(x)=2

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 (16)^(x)=2 | Equatix

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$${ 16 }^{ x } =2$$

$x=\frac{1}{4}=0.25$

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

$$16^{x}=2$$

Take the logarithm of both sides of the equation.

$$\log(16^{x})=\log(2)$$

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

$$x\log(16)=\log(2)$$

Divide both sides by $\log(16)$.

$$x=\frac{\log(2)}{\log(16)}$$

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

$$x=\log_{16}\left(2\right)$$

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