Question

evaluate: log 16 to the base 0.5

Answer 1

Heya user,

---->[tex]log_{0.5}16 = log_{0.5} [2]^4 [/tex]
----->$= 4log_{0.5} [ 1/2]^{-1}$
----->$4 log_{0.5} [0.5]^{-1}$
===> 4 * -1 * $log_{0.5} [0.5]$
===> -4 * 1 = -4

Answer 2

The value of $\log_{0.5} 16=-4$

Step-by-step explanation:

We have,

$\log_{0.5} 16$

To find, the value of $\log_{0.5} 16=?$

∴ $\log_{0.5} 16$

$=\log_{0.5} 2^{4}$

$=\log_{0.5} \dfrac{1}{2^{-4}}$

Using the formula,

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

$=\log_{0.5} (\dfrac{1}{2})^{-4}$

$=(-4)\log_{0.5} (\dfrac{1}{2})$

Using the formula,

$\log a^{m} =m\log a$

$=(-4)\log_{0.5} 0.5$

= - 4 × 1

Using the formula,

$\log_a a =1$

= - 4

The value of $\log_{0.5} 16=-4$

Hence, the value of $\log_{0.5} 16=-4$