Question

find log16 base 1/2​

Answer 1

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Answer 2

$\displaystyle \sf{ log_{ \frac{1}{2} }(16) } = - 4$

Given :

The expression

$\displaystyle \sf{ log_{ \frac{1}{2} }(16) }$

To find :

Simplify the given expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ log_{ \frac{1}{2} }(16) }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{ log_{ \frac{1}{2} }(16) }$

$\displaystyle \sf{ = \frac{ log \: 16 }{ log \: \frac{1}{2} } }$

$\displaystyle \sf{ = \frac{ log \: {2}^{4} }{ log \: 1 -log \: 2} }$

$\displaystyle \sf{ = \frac{4 log \: {2}^{} }{ 0 -log \: 2} }$

$\displaystyle \sf{ = \frac{4 log \: {2}^{} }{ -log \: 2} }$

$\displaystyle \sf{ = - \frac{4 log \: {2}^{} }{ log \: 2} }$

$\displaystyle \sf{ = - 4 }$

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