Question

Write -5 as a logarithim with a base of 4

Answer 1

Answer:

$log_4(\frac{1}{4^5}) = -5$

Step-by-step explanation:

$log_b(a) = c$ ↔ $b^c = a$

You are given $b$ = 4

You re also given $c$ = -5

To find a, use the exponential form:

$b^c = a$

$= (4)^{-5} = \frac{1}{4^5} = a$

Then you can convert into a logarithm.

$log_4(\frac{1}{4^5}) = -5$

Answer 2

Answer:

There are multiple ways of writing this:

$\sf -5log_4(4)=log_4(4^{-5})=log_4\left(\dfrac{1}{4^5}\right)=log_4\left(\dfrac{1}{1024}\right)$

Step-by-step explanation:

Log rule:  $\sf log_a(a)=1$

$\sf \implies log_4(4)=1$

$\sf \implies -5log_4(4)=-5$

Log rule:  $\sf c \cdot log_ab=log_a(b^c)$

$\sf \implies -5log_4(4)=log_4(4^{-5})$

                       $\sf = log_4\left(\dfrac{1}{4^5}\right)$

                       $\sf = log_4\left(\dfrac{1}{1024}\right)$