1/（log3 √15）+1/（log5 √15）
=1/（1/2*log3 15）+1/（1/2*log5 15）
=2/（log3 15）+2/（log5 15）
=2/[log3 (3*5)]+2/[log5 (3*5）]
=2/[log3 3 +log3 *5]+2/[log5 3 +log5 5]
=2/[1+log3 *5]+2/[1+log5 3]
=2/[1+log3 *5]+2/[1+1/log3 5]
=2/[1+log3 *5]+2log3 5/[1+log3 5]
=[2+2log3 5]/[1+log3 5]
=2[1+log3 5]/[1+log3 5]
=2