Numbers can be expressed in logarithms.
The value of [tex]\mathbf{log_248}[/tex] is [tex]\mathbf{k + 4}[/tex]
The expressions are given as:
[tex]\mathbf{k = log_23}[/tex]
[tex]\mathbf{log_248}[/tex]
Express 48 as 3 * 16
[tex]\mathbf{log_248 = log_2(3 \times 16)}[/tex]
Split
[tex]\mathbf{log_248 = log_2(3) + log_2(16)}[/tex]
Express 16 as 2^4
[tex]\mathbf{log_248 = log_2(3) + log_2(2^4)}[/tex]
Rewrite as:
[tex]\mathbf{log_248 = log_2(3) + 4log_22}[/tex]
In logarithms:
[tex]\mathbf{log_aa = 1}[/tex]
So, we have:
[tex]\mathbf{log_248 = log_2(3) + 4(1)}[/tex]
[tex]\mathbf{log_248 = log_2(3) + 4}[/tex]
Substitute [tex]\mathbf{k = log_23}[/tex]
[tex]\mathbf{log_248 = k + 4}[/tex]
Hence, the value of [tex]\mathbf{log_248}[/tex] is [tex]\mathbf{k + 4}[/tex]
Read more about logarithms at:
https://brainly.com/question/8657113
