Question

write the equation in logarithmic form.
$81^{\frac{1}{4}} = 3$
$81^{\frac{1}{4}} = 3$ written in logarithmic form is $\square$.

Explanation:

Step1: Recall the exponential - logarithmic conversion formula

The exponential form \(a^{x}=y\) can be converted to the logarithmic form \(\log_{a}y = x\), where \(a>0,a
eq1\), \(x\) is any real number, and \(y > 0\).

Step2: Identify \(a\), \(x\), and \(y\) from the given equation

In the equation \(81^{\frac{1}{4}}=3\), we have:

• The base \(a = 81\) (since in the exponential form \(a^{x}\), the base is \(a\)).
• The exponent \(x=\frac{1}{4}\) (since in \(a^{x}\), the exponent is \(x\)).
• The result \(y = 3\) (since in \(a^{x}=y\), the right - hand side is \(y\)).

Step3: Apply the conversion formula

Using the formula \(\log_{a}y=x\) with \(a = 81\), \(x=\frac{1}{4}\), and \(y = 3\), we get \(\log_{81}3=\frac{1}{4}\).

Answer:

\(\log_{81}3=\frac{1}{4}\)