b) Complete the statements
i) $\log _{\frac{1}{9}} x=$
ii) $\log _{81} x=$
$\log _{9} x$
$\log _{3} x=$
$\log _{9} x$

Step 1 ：The general form of a logarithm function is \(\log_b x = y\), which means \(b^y = x\). In this case, \(b\) is the base of the logarithm, \(x\) is the argument of the logarithm, and \(y\) is the value of the logarithm.

Step 2 ：For the first statement, \(\log_{\frac{1}{9}} x\), the base of the logarithm is \(\frac{1}{9}\), and the argument is \(x\). We don't know the value of \(x\), so we can't calculate the value of the logarithm.

Step 3 ：For the second statement, \(\log_{81} x\), the base of the logarithm is \(81\), and the argument is \(x\). Again, we don't know the value of \(x\), so we can't calculate the value of the logarithm.

Step 4 ：For the third statement, \(\log_{9} x\), the base of the logarithm is \(9\), and the argument is \(x\). Once again, we don't know the value of \(x\), so we can't calculate the value of the logarithm.

Step 5 ：For the fourth statement, \(\log_{3} x\), the base of the logarithm is \(3\), and the argument is \(x\). Yet again, we don't know the value of \(x\), so we can't calculate the value of the logarithm.

Step 6 ：For the fifth statement, \(\log_{9} x\), this is a repeat of the third statement.

Step 7 ：Without knowing the value of \(x\), we can't calculate the value of these logarithms.

Step 8 ：Final Answer: Without specific values for \(x\), the completed statements are as follows:

Step 9 ：i) \(\log _{\frac{1}{9}} x = y\), where \(y\) is such that \((\frac{1}{9})^y = x\)

Step 10 ：ii) \(\log _{81} x = y\), where \(y\) is such that \(81^y = x\)

Step 11 ：iii) \(\log _{9} x = y\), where \(y\) is such that \(9^y = x\)

Step 12 ：iv) \(\log _{3} x = y\), where \(y\) is such that \(3^y = x\)

Step 13 ：v) \(\log _{9} x = y\), where \(y\) is such that \(9^y = x\)