Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 175420 by Linton last updated on 30/Aug/22

solve for x 2^x .3^x^2 = 6

solveforx2x.3x2=6

Answered by Rasheed.Sindhi last updated on 30/Aug/22

2^x .3^x^2 = 6 log(2^x )+log(3^x^2 )=log(6) xlog(2)+x^2 log(3)−log(6)=0 x=((−log(2)±(√(log^2 (2)+4(log(3)(log(6))))/(2log(3)))

2x.3x2=6log(2x)+log(3x2)=log(6)xlog(2)+x2log(3)−log(6)=0x=−log(2)±log2(2)+4(log(3)(log(6)2log(3)

Commented by henderson last updated on 30/Aug/22

i prefer this way.

ipreferthisway.

Commented by Linton last updated on 30/Aug/22

this is the exact solutions

thisistheexactsolutions

Commented by BaliramKumar last updated on 30/Aug/22

2^x .3^x^2 = 6 log(2^x )+log(3^x^2 )=log(6) xlog(2)+x^2 log(3)−log(6)=0 x=((−log(2)±(√(log^2 (2)+4log(3)log(6))))/(2log(3))) x=((−log(2)±(√(log^2 (2)+4log(3)[log(2)+log(3)])))/(2log(3))) x=((−log(2)±(√(log^2 (2)+4log(2)log(3)+4log^2 (3))))/(2log(3))) x=((−log(2)±(√([log(2)+2log(3)]^2 )))/(2log(3))) x=((−log(2)±[log(2)+2log(3)])/(2log(3))) x_1 = ((−log(2)+[log(2)+2log(3)])/(2log(3))) x_2 = ((−log(2)−[log(2)+2log(3)])/(2log(3))) x_1 = ((2log(3))/(2log(3))) = 1 & x_2 = − ((log(2)+log(3))/(log(3))) = − ((log(6))/(log(3))) x_1 = 1 & x_(2 ) = − log_3 (6) determinant ()