Question

What is the value of log0.5 16 (0.5 is the small bottom number)-4.00-0.251.512.41

Answer 1

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

$log_a(b) = \frac{log a}{log b}$

$4 log_{2^-1}(2)=4 \frac{log 2}{log 2^-1}$

Move the exponent -1 before log

$4 \frac{log 2}{-1log 2}$

log 2 will get cancelled

$\frac{4}{-1}$

-4

-4.00 is the final answer

Answer 2

we are given

$log_0_._5(16)$

Firstly, we will factor out 16

$16=2\times 2\times 2\times 2\times 2$

$16=2^4$

we can write it as

$16=(\frac{1}{2})^{-4}=(0.5)^{-4}$

we can replace it as

$log_0_._5(16)=log_0_._5((\frac{1}{2})^{-4})$

now, we can use property of log

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

we get

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

$log_0_._5(16)=-4\times 1$

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