Answer:
[tex]\log_{\frac{1}{2}} 5=-2.32193[/tex]
Step-by-step explanation:
Given : Expression [tex]\log_{\frac{1}{2}} 5[/tex]
To find : The solution of the given expression ?
Solution :
We have given expression [tex]\log_{\frac{1}{2}} 5[/tex]
Applying logarithmic property,
[tex]\log_b a=\frac{\log_e a}{\log_e b}=\frac{\ln a}{\ln b}[/tex]
Where, [tex]\log _e[/tex] is the natural logarithm indicated as [tex]\ln[/tex]
[tex]\log_{\frac{1}{2}} 5=\frac{\ln (5)}{\ln {\frac{1}{2}}}[/tex]
[tex]\frac{\ln (5)}{\ln {\frac{1}{2}}}=\frac{1.60943}{ -0.69315}[/tex]
[tex]\frac{\ln (5)}{\ln {\frac{1}{2}}}=-2.32193[/tex]
Therefore, [tex]\log_{\frac{1}{2}} 5=-2.32193[/tex]
