Question

Solve log4 (y − 9) + log4 3 = log4 81

Answer 1

Answer: y = 36

Step-by-step explanation:

This is question on logarithm, so it is logarithmic equation.

Log4(y - 9) + log4 3 = log4 81

Now remembered that in logarithm, it is the opposite of the indices. The addition in log. means multiplication. So, log 4(y -9) + log 4 3 = log4{(y - 9)× 3}

So, log4{(y - 9) × 3 = log4 81

Now since log 4 is common, divide everything by log 4 leave the equation

3( y - 9 ) = 81

3y - 27. = 81

3y = 81 + 27

3y = 108

y = 108/3

y = 36.

Answer 2

Answer:

y = 36

Step-by-step explanation:

log4 (y − 9) + log4 3 = log4 81

We know that loga (b) + loga ( c) = loga ( b*c)

log4 (y − 9) * 3 = log4 81

We know have loga ( BC ) = loga ( d)

This means BC = d

(y − 9) * 3  = 81

Divide each side by 3

y - 9 = 81/3

y - 9 = 27

Add 9 to each side

y-9+9 = 27+9

y = 36