what is value of x in an arithmetic progression involving logarthms $\log 2,\log 2^{x-1}$, and $\log 2^{x+3}$ are $3$ consecutive terms of an arithmetic progression; find  (i) the value of $x$;

Using $\log(a^b)=b\log a$ and dividing by $\log2$ we see that $1,x-1,x+3$ must be an arithmetic progression. But it's clear that $x-5,x-1,x+3$ is an arithmetic progression. So $x\dots$
