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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


Answered by Henry X. Maths tutor

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