Solve for x in this (A.P) ifl

Question

Solve for x in this (A.P) if $\log x + \log x^2 +\log x^3 .......+ \log x^n = n(n+1)$ So what I have found is a common difference, d is log x and a = log x but how do I solve for x??? the sum of this ap is n(n+1) i think

Answer 1

The sum of an $AP$ that increment by $1$ from $1$ to $n$ is $\frac{n(n+1)}2$.

Hence the problem reduces to $$\frac{n(n+1)}{2}\log x=n(n+1)$$

$$n(n+1)\log x=2n(n+1)$$

Hopefully you can simplify and solve for $x$ now.