Question

What is the value of log0.5 16?

Answer 1

Answer:

log_0.5(16)=-4

Step-by-step explanation:

log_0.5(16)

0.5 can be written as 1/2

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

We apply log property

$log_{a^{-b}}(x)=\frac{1}{b}log_a(x)$

so $log_{2^{-1}}(16)=-1log_2(16)$

Now  we write 16 in exponential form

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

$-1log_2(16)=-1log_2(2^4)$

log a^m = m log (a),and log_a(a)= 1 Apply these properties

-1*4 log_2(2)

-1*4(1)= -4

Answer 2

 the answers is -4 ... i think