If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$, then $x$ is equal to:

Let $\phi (x) = x + 2^{\log_x 3} - 3^{\log_x 2}$. Then which of the following is true?

The solution set of the equation $\left| {1 - {{\log }_{1/6}}x} \right| + \left| {{{\log }_2}x} \right| + 2 = \left| {3 - {{\log }_{1/6}}x + {{\log }_{1/2}}x} \right|$ is $\left[ {\frac{a}{b},a} \right]$,where $a, b \in N$. Then the value of $(a + b)$ is:

The logarithm of $32\sqrt[5]{4}$ to the base $2\sqrt{2}$ is:

The value of $\log_2(\log_3(\dots(\log_{100}(100^{99^{98^{\dots^{2^1}}})))\dots))}$ is

If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then find the value of ${\log _3}2$.