Question

What is the value of log0.5 16 (0.5 is the small bottom number)

-4.00
-0.25
1.51
2.41

Answer 1

we are given

`log_0_._5(16)`

Firstly, we will factor out 16

`16=2* 2* 2* 2* 2`

`16=2^4`

we can write it as

`16=((1)/(2))^(-4)=(0.5)^(-4)`

we can replace it as

`log_0_._5(16)=log_0_._5(((1)/(2))^(-4))`

now, we can use property of log

`log_a(b^n)=nlog_a(b)`

we get

`log_0_._5(16)=-4log_0_._5(0.5)`

`log_0_._5(16)=-4* 1`

`log_0_._5(16)=-4`.............Answer

Answer 2

Answer : -4.00

what is the value of
`log_(0.5)(16)`

We use log property to find the value

16 = 2*2*2*2 = 2^4

So we replace 16 by 2^4

`log_(0.5)(2^4)`

As per log property we move exponent before log

`4 log_(0.5)(2)`

0.5 can be written as 1/2 . 1/2 can be written as 2^-1

`4 log_(2^-1)(2)`

Now we apply change of base formula

`log_a(b) = (log a)/(log b)`

`4 log_(2^-1)(2)=4 (log 2)/(log 2^-1)`

Move the exponent -1 before log

`4 (log 2)/(-1log 2)`

log 2 will get cancelled

`(4)/(-1)`

-4

-4.00 is the final answer