Answer:
The value of y is, 36
Step-by-step explanation:
Using logarithmic rules:
[tex]\log_b m+ \log_b n = \log_b (mn)[/tex]
if [tex]\log_b x = \log_b y[/tex] then, x = y
As per the statement:
Given the equation:
[tex]\log_4 (y-9)+\log_4 3 = \log_4 81[/tex]
Apply the logarithmic rules;
[tex]\log_4 3(y-9) = \log_4 81[/tex]
Apply the logarithmic rules; we have;
[tex]3(y-9) = 81[/tex]
Divide both sides by 3 we have;
[tex]y-9 = 27[/tex]
Add 9 to both sides we have;
y = 36
Therefore, the value of y is, 36
