Question

Plzzz solv it fast vii convert into exponential form and answer is - 8

Answer 1

log (256 base 0.5)

= log( 2^8 base 2^-1)


we know concept
log( a base c^x ) = 1/x log( a base c )

also log( a^x base a ) = x log( a base a )
= x

use both concept here

- log(2^8 base 2)

= -8 ( answer )

Answer 2

1)256= 2^8
2)0.5= 5/10=1/2=2^-1
We are using below laws
3)log a^n= n*log a
4)log a^m base a^n = m/n *log a base a
5)log a base a =1
Now
log 256 base 0.5 = log 2^8 base 2^-1

= 8/(-1) log 2 base 2
= -8