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:

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