If $$n = (2017)!$$, then what is $${1 \over {{{\log }_2}n}} + {1 \over {{{\log }_3}n}} + {1 \over {{{\log }_4}n}} + ... + {1 \over {{{\log }_{2017}}n}}$$ equal to?

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?