Question

submitting an external tool

$-4log_4(x)+1 = 13$

answer attempt 1 out of 2

$x =$

Explanation:

Step1: Isolate the logarithmic term

Subtract 1 from both sides of the equation:

$$-4\log_4(x)=13 - 1$$

$$-4\log_4(x)=12$$

Step2: Solve for the logarithmic term

Divide both sides by - 4:

$$\log_4(x)=\frac{12}{-4}=-3$$

Step3: Convert to exponential form

Using the definition of logarithms \(y = \log_a(x)\) is equivalent to \(x=a^y\), we have:

$$x = 4^{-3}$$

$$x=\frac{1}{4^3}=\frac{1}{64}$$

Answer:

\(\frac{1}{64}\)