que 11 11 Solve the equations (i) log5x4 + 5 - log1/5 x2 + 25 = - Maths - Relations and Functions

Question

que 11

11     Solve   the   equations   ( i )
  log 5 x 4   +   5   -   log 1 / 5  
x 2   +   25   =   3 2 ( ii )     log
5 x 4   +   5   -   log 1 / 5   x 2  
+   25   =   3

Aarushi Mishra · Accepted Answer

i
log5x4+5-log1/5x2+25=32log5x4+5-log5-1x2+25=32Use logamb=1mlogablog5x4+5+log5x2+25=32Use logam+logan=logamnlog5x4+5x2+25=32x4+5x2+25=532x4+5x2+25=55Nowx2+25≥25x4+5≥5Multiplyingx2+25x4+5≥125Thereforex4+5x2+25=55 has no solutionii
log5x4+5-log1/5x2+25=3log5x4+5-log5-1x2+25=3Use logamb=1mlogablog5x4+5+log5x2+25=3Use logam+logan=logamnlog5x4+5x2+25=3x4+5x2+25=53x4+5x2+25=125Nowx2+25≥25x4+5≥5Multiplyingx2+25x4+5≥125125 is the minimum value of product which will occur when x2+25 and x4+5 are both minimumi
e
 when x2+25=25, and x4+5=5So x=0 is the solution

que 11 11 . Solve the equations ( i ) log 5 x 4 + 5 - log 1 / 5 x 2 + 25 = 3 2 ( ii ) log 5 x 4 + 5 - log 1 / 5 x 2 + 25 = 3

que 11

$11 . Solve the equations (i) \log_{5} (x^{4} + 5) - \log_{1 / 5} (x^{2} + 25) = \frac{3}{2} (ii) \log_{5} (x^{4} + 5) - \log_{1 / 5} (x^{2} + 25) = 3$