Solve 2 ^ x = 1/16 the table for v = 4 ^ x | 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

$$2 ^ { x } = \frac { 1 } { 16 }$$

Solve for x

$x=-4$

Steps Using Definition of Logarithm

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

$$2^{x}=\frac{1}{16}$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(\frac{1}{16})$$

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

$$x\log(2)=\log(\frac{1}{16})$$

Divide both sides by $\log(2)$.

$$x=\frac{\log(\frac{1}{16})}{\log(2)}$$

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

$$x=\log_{2}\left(\frac{1}{16}\right)$$

Solve for x (complex solution)

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