Question

What is the value of log0.5 16

Answer 1

The answer:
the full question is as follow 
What is the value of log0.5 ^16

first of all, we should know some logarithm property
for example:
log a^p = p log a, for all a a positive number, an p a real number

therefore, log0.5 ^16 = 16log0.5, and log0.5 = -0.69, 
finally
log0.5 ^16 = 16log0.5=16*(-0.69)= -11

Answer 2

Answer:

You mean ?

$log_0_._5 (16) =-4$

or

You mean?

$log(0.5)^{16}=-11.09035489$

Step-by-step explanation:

If you trying to solve:

$log_0_._5(16)$

Then use the definition of the base of a log which is:

$log_xy=z\Rightarrow x^z=y$

$0.5^z=16$  

Rewrite 0.5 as:

$0.5=\frac{1}{2}$

As you may know:

$2^4=16$

$then\\\\z=-4$

Let's use the negative exponent propierty in order to verify the result:

$a^{-n}=\frac{1}{a^n}$

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

If you trying to solve:

$log(0.5)^{16}$

Then use reduction of power propierty:

$log(x^y)=y log(x)$

Therefore:

$log(0.5)^{16} =16 *log(0.5)=16*(-0.6931471806)=-11.09035489$