Respuesta :
Answer:
log_0.5(16)=-4
Step-by-step explanation:
log_0.5(16)
0.5 can be written as 1/2
[tex]log_\frac{1}{2} (16) = log_{2^{-1}}(16)[/tex]
We apply log property
[tex]log_{a^{-b}}(x)=\frac{1}{b}log_a(x)[/tex]
so [tex]log_{2^{-1}}(16)=-1log_2(16)[/tex]
Now we write 16 in exponential form
16= 2*2*2*2 = 2^4
[tex]-1log_2(16)=-1log_2(2^4)[/tex]
log a^m = m log (a),and log_a(a)= 1 Apply these properties
-1*4 log_2(2)
-1*4(1)= -4
