Question

log x base 2 + log 2 base x = 4.25 then log x base 4 + log 4 base x = ?​

Answer 1

Answer:

1) log x ( base 4) = log x/ log 4

= logx /log 2²

log x/( 2log 2) =

= 1/2 x log x ( base 2)

2) log x (base 16 )

= logx /log 16

= log x / log 24

= log x /4log2

= 1/4 x log x (base 2)

Now,

log x( base 2) + logx ( base 4) + logx( base 2) = = 21/4

log x ( base 2 ) + 1/2 [ logx ( base 2 )] + 1/4[log( base 2)] = 21/4

logx (base 2) [1+1/2 + 1/4 ] = 21/4

log x( base 2) [(4 +2+1)/4 ] = 21/4

(7/4) log x ( base 2) = 21/4

log x ( base 2) = (21 × 4 )/ ( 4 × 7 )

log x ( base 2) = 3

x = 2³

x = 8

#shreya

Answer 2

Answer:

all problems are not only solved by calculation

some are solved by assuming also

in this problem

if we take ,

x=16, log (base2) 16+ log(base16) 2= 4+1/4=4+0.25=4.25

then,

log( base4) 16 + log(base16) 4 = 2+1/2 = 2+0.5

=2.5