Question

change the exponential statement to an equivalent statement involving a logarithm.
6.5 = 9^x
the equivalent logarithmic statement is \boxed{}.
(type an equation. use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Recall the exponential - logarithmic conversion formula

The general formula for converting an exponential equation \(y = a^{x}\) (where \(a>0,a
eq1\)) to a logarithmic equation is \(\log_{a}y=x\).

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

In the given exponential equation \(6.5 = 9^{x}\), we have \(y = 6.5\), \(a=9\) and \(x\) (the exponent in the exponential form which will be the result in the logarithmic form).

Step3: Apply the conversion formula

Using the formula \(\log_{a}y=x\), substituting \(y = 6.5\), \(a = 9\) and \(x\) (the variable), we get \(\log_{9}(6.5)=x\).

Answer:

\(\log_{9}(6.5)=x\)