Examine whether the series \(\sum_1^∞=(\log n)^{\log n}\) is convergent.

\(\displaystyle{n}={2}\)

If \(\log_{2} (6x + 6) = 5, \text{then}\ x =?\)

\(\ln(x − 2) = 5\) in exponential form

solve the equation \(\log(base16)(3x-1)= \log(base4)(3x)+\log(base4)0.5\)?

Write \(\log_3 \frac{1}{27x^{2}}\) in the form a+b \(\log_3x\) where a and b are integers

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. \(\displaystyle{\log_{2}}{\left({3}{x}−{1}\right)}={\log_{2}}{\left({x}+{1}\right)}+{3}\)