what is the value of $log_{0.5}16$?\n-4.00\n-0.25\n1.51\n2.41

Explanation:

Step1: Use change - of - base formula

$\log_{a}b=\frac{\ln b}{\ln a}$, so $\log_{0.5}16 = \frac{\ln 16}{\ln 0.5}$

Step2: Calculate natural logarithms

We know that $\ln 16=\ln(2^4) = 4\ln 2$ and $\ln 0.5=\ln(\frac{1}{2})=-\ln 2$.

Step3: Substitute values

$\frac{\ln 16}{\ln 0.5}=\frac{4\ln 2}{-\ln 2}=- 4$

Answer:

-4.00