Solve (1/4) ^ (x + 1) = 1/64 | 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

$$(\frac{1}{4})^{x+1}=\frac{1}{64}$$

Solve for x

$x=2$

Steps Using Definition of Logarithm

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

$$\left(\frac{1}{4}\right)^{x+1}=\frac{1}{64}$$

Take the logarithm of both sides of the equation.

$$\log(\left(\frac{1}{4}\right)^{x+1})=\log(\frac{1}{64})$$

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

$$\left(x+1\right)\log(\frac{1}{4})=\log(\frac{1}{64})$$

Divide both sides by $\log(\frac{1}{4})$.

$$x+1=\frac{\log(\frac{1}{64})}{\log(\frac{1}{4})}$$

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

$$x+1=\log_{\frac{1}{4}}\left(\frac{1}{64}\right)$$

Subtract $1$ from both sides of the equation.

$$x=3-1$$

Solve for x (complex solution)

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