Let \(x\) be an odd integer greater than 1, and let \(b=x-1\). The equation \(\log_b a=x\) is true. Which of the following phrases describes every value of \(a\) ?

Summary Submit Skip Question

$$ \log_b a=x $$

Rewriting in exponential form:

$$ b^x = a $$

Because \(b=x-1\),

$$ (x-1)^x = a $$

Since \(x\) is odd and greater than 1, \(x-1\) will always be even. Taking any even number to any power results in an even nonzero number. We should verify this by trying out some values of \(x\).