Exponential and Logarithmic Functions

If $\log_b(81) = 4$, what is the value of $b$?

What are possible domain restrictions for $g(x)=\ln \left( -\frac{x}{4} \right)$?

What does the graph of $y=\log_{5}(x)$ look like for $x>0$?

What does $\log_b(b)$ equal?

What is $\log_{10}(y)$ equal to if its corresponding exponential form is represented as $10^n = y$?

When does the inequality $\log_{p}(m) \times \log_{q}(n) > 0$ hold true given $m,n,p,q > 0$ and $p,q$ not equal to 1?

If the amount of a radioactive substance decays exponentially and the half-life of the substance is known to be 5 years, which function best models the remaining amount $y(t)$ in grams after $t$ years if initially there were 20 grams?

What does "log" generally stand for in mathematical notation?

If $y = \log_{e} x$, then for which value of $x$ would $y$ be equal to one?

How do you rewrite the equation $\ln(x)=7$ as an exponential function?