If $$x + {\log _{15}}(1 + {3^x}) = x{\log _{15}}5 + {\log _{15}}12$$, where x is an integer, then what is x equal to?

If 0 < a < 1, the value of log₁₀ a is negative. This is justified by

If $${x^{{{\log }_7}x}} > 7$$ where x > 0, then which one of the following is correct?

If $\log _b a=p, \log _d c=2 p$ and $\log _f e=3 p$, then what is $(a c e)^{\frac{1}{p}}$ equal to ?