Question

solve for x.
-3 + \log_{3}(4x) = 1
x = \square

Explanation:

Step1: Isolate the logarithmic term

Add 3 to both sides of the equation \(-3 + \log_{3}(4x) = 1\).
We get \(\log_{3}(4x)=1 + 3\), which simplifies to \(\log_{3}(4x)=4\).

Step2: Convert logarithmic to exponential form

Recall that if \(\log_{a}(b)=c\), then \(a^{c}=b\). Here, \(a = 3\), \(c = 4\), and \(b = 4x\).
So we have \(3^{4}=4x\).

Step3: Calculate \(3^{4}\) and solve for \(x\)

Calculate \(3^{4}=81\). Then the equation becomes \(81 = 4x\).
Divide both sides by 4: \(x=\frac{81}{4}\).

Answer:

\(\frac{81}{4}\)