log_10⁡((1/(2√2))*(p+2q))=(1/2)(log_10⁡p+log_10⁡q),p,q>0,find p in terms of q.

log₁₀[(1/2√2)(p+2q)]=(1/2)(log₁₀p+log₁₀q)log₁₀[(1/2√2)(p+2q)]=(1/2)(log₁₀pq)log₁₀[(1/2√2)(p+2q)]=log₁₀(pq)^1/2(1/2√2)(p+2q)=(pq)^1/2(p+2q)²=8pqp²+4pq+4q²=8pqp²-4pq+4q²=0(p-2q)=0thus => p=2q