If x, y, z are the 10th, 13th and 15th terms of a G.P. find the value of
Det =| log x     10    1|
         | log y     13    1|
         | log z     15    1|

Dear Student,
Please find below the solution to the asked query:

 x,y,z are 10th, 13th and 15th term.Let a be first term and r be common ratio, hencex=ar9y=ar12z=ar14logx101logy131logz151=logar9101logar12131logar14151=loga+logr9101loga+logr12131loga+logr14151=loga+9logr101loga+12logr131loga+14logr151On splitting the first colmum we get=loga101loga131loga151+9logr10112logr13114logr151Take loga common in first determinant and logr in second=loga110111311151+logr91011213114151C1 and C3 are same in first determinant, hence it becomes 0, in seconddeterminant C1C1+C3=0+101011313115151=0+0+=0 Answer

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