Question

Evaluate the logarithm

Answer 1

\[\log _{4} 1024\]

Answer 2

A. 5
B. -5
C. 4
D. 6

Answer 3

A. 5 is the answer \[4^x =1024\] x=5

Answer 4

$$
\log_41024=y\\
\implies 1024=4^y\\
\log_2 1024=\log_2 4^y=y~\log_2 4\\
y=\cfrac{\log_2 1024}{\log_2 4}=\cfrac{10}{2}=5
$$
Where \(log_2 x\) is the log is base of 2 of \(x\). I used base 2 for this converstion because I noticed that 1024 and 4 are easily represented by \(2^x\) for some \(x\). Use natural logs if \(e\) is involved or base 10 is numbers are in powers of 10, such as 1 000, or 1 000 000.

Therefore,
$$
\log_4 1024=5
$$
http://www.wolframalpha.com/input/?i=log+base+4+1024

Answer 5

THnks

Answer 6

yw