Answer:
[tex]log_4(\frac{1}{4^5}) = -5[/tex]
Step-by-step explanation:
[tex]log_b(a) = c[/tex] ↔ [tex]b^c = a[/tex]
You are given [tex]b[/tex] = 4
You re also given [tex]c[/tex] = -5
To find a, use the exponential form:
[tex]b^c = a[/tex]
[tex]= (4)^{-5} = \frac{1}{4^5} = a[/tex]
Then you can convert into a logarithm.
[tex]log_4(\frac{1}{4^5}) = -5[/tex]
Answer:
There are multiple ways of writing this:
[tex]\sf -5log_4(4)=log_4(4^{-5})=log_4\left(\dfrac{1}{4^5}\right)=log_4\left(\dfrac{1}{1024}\right)[/tex]
Step-by-step explanation:
Log rule: [tex]\sf log_a(a)=1[/tex]
[tex]\sf \implies log_4(4)=1[/tex]
[tex]\sf \implies -5log_4(4)=-5[/tex]
Log rule: [tex]\sf c \cdot log_ab=log_a(b^c)[/tex]
[tex]\sf \implies -5log_4(4)=log_4(4^{-5})[/tex]
[tex]\sf = log_4\left(\dfrac{1}{4^5}\right)[/tex]
[tex]\sf = log_4\left(\dfrac{1}{1024}\right)[/tex]
