Question

If logx to the base 2 + logx to the base 4 + logx to the base 16 = 21/4, then x is equal to

Answer 1

answer is 8 by sloving it

Answer 2

Hi ,

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

= logx /log 2²

= log x/( 2log 2)

= 1/2 × log x ( base 2 )

2 ) log x ( base 16 )

= logx /log 16

= log x / log 2⁴

= log x /4log2

= 1/4 × 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

I hope this helps you.

: )