Change the exponential statement to an equivalent statement involving a logarithm. \[ e^{\mathrm{x}}=12 \] The equivalent logarithmic statement is \( \square \). (Type an equation.)

Indicate between which two integers the following root lies \( ?<\sqrt{13}< \) ?

The doubling period of a bacterial population is 15 minutes. At time \( t=80 \) minutes, the bacterial population was 60000 . What was the initial population at time \( t=0 \) ? Find the size of the bacterial population after 4 hours.

2. The value of \( \frac{(0.1)^{2}-(0.01)^{2}}{0.0001}+1 \) is

Agar \( a=(\sqrt{3}+1)^{4} \) bo'lsa, \( a \cdot(1-\{a\}) \) ning qiymatini toping. Bu yerda \( \{a\}-a \) sonining kasr qismi. \( \begin{array}{llll}\text { A) } 1 & \text { B) } 81 & \text { C) } 54 & \text { D) } 16\end{array} \)

Simplify without a Calculator \[ \log _{5}\left(\frac{1}{625}\right)=\square \]