Question

write the following logarithmic equation as an exponential equation. do not simplify your answer. \\(\log_{x}(3.9) = 6\\)

Explanation:

Step1: Recall the logarithmic to exponential conversion rule

The logarithmic equation \(\log_{b}(a) = c\) can be converted to the exponential equation \(b^{c}=a\) (where \(b>0\), \(b
eq1\)).

Step2: Apply the rule to the given equation

In the given equation \(\log_{x}(3.9) = 6\), we identify \(b = x\), \(a=3.9\) and \(c = 6\). Using the conversion rule \(b^{c}=a\), we substitute the values to get \(x^{6}=3.9\).

Answer:

\(x^{6}=3.9\)