Question

write equation in its equivalent exponential form
log₄ x = 3

Explanation:

Step1: Recall Logarithm Definition

The logarithmic equation \(\log_{b}a = c\) is equivalent to the exponential equation \(b^{c}=a\) (by the definition of logarithms, where \(b>0,b
eq1\)).

Step2: Apply to Given Equation

For the equation \(\log_{4}x = 3\), we identify \(b = 4\), \(c = 3\), and \(a=x\). Using the equivalence from Step 1, we substitute these values into the exponential form. So we get \(4^{3}=x\).

Answer:

\(4^{3}=x\) (or \(x = 4^{3}\) which simplifies to \(x = 64\), but the equivalent exponential form is \(4^{3}=x\))