Verified Answer :

meerkat18

Take note that log mn may also be expressed as log m + log n. So, for the given,
                         log4 (y - 9)(3) = log4 81
Dropping the log4 leaves us with,
                                 (y - 9)(3) = 81
The value of y from the equation is 36.

Answer:

The value of y is, 36

Step-by-step explanation:

Using logarithmic rules:

\(\log_b m+ \log_b n = \log_b (mn)\)

if \(\log_b x = \log_b y\) then, x = y

As per the statement:

Given the equation:

\(\log_4 (y-9)+\log_4 3 = \log_4 81\)

Apply the logarithmic rules;

\(\log_4 3(y-9) = \log_4 81\)

Apply the logarithmic rules; we have;

\(3(y-9) = 81\)

Divide both sides by 3 we have;

\(y-9 = 27\)

Add 9 to both sides we have;

y = 36

Therefore, the value of y is, 36

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