Answer :
Let's solve each of these logarithmic expressions. Remember, a logarithm can be defined as the exponent to which the base must be raised to produce a given number.
k) [tex]\log_4 16[/tex]
To solve [tex]\log_4 16[/tex], you need to determine what power 4 must be raised to in order to get 16.
First, express 16 as a power of 4:
16 = 4^2
So, [tex]\log_4 16 = 2[/tex].
l) [tex]\log_4 64[/tex]
To solve [tex]\log_4 64[/tex], express 64 as a power of 4.
Since 64 = 4^3,
[tex]\log_4 64 = 3[/tex].
m) [tex]\log_4 256[/tex]
To find [tex]\log_4 256[/tex], express 256 as a power of 4.
256 = 4^4
Therefore, [tex]\log_4 256 = 4[/tex].
n) [tex]\log_5 25[/tex]
To solve [tex]\log_5 25[/tex], you want to express 25 as a power of 5.
Since 25 = 5^2,
[tex]\log_5 25 = 2[/tex].
o) [tex]\log_5 125[/tex]
Finally, for [tex]\log_5 125[/tex], express 125 as a power of 5.
125 = 5^3
Therefore, [tex]\log_5 125 = 3[/tex].
In summary, here are the solutions to the logarithmic expressions:
k) [tex]\log_4 16 = 2[/tex]
l) [tex]\log_4 64 = 3[/tex]
m) [tex]\log_4 256 = 4[/tex]
n) [tex]\log_5 25 = 2[/tex]
o) [tex]\log_5 125 = 3[/tex]