The relationship of log aⁿ = n × log a is used. Then the value of a is negative 3.67.
Logarithms are another way of writing exponent. A logarithm with a number base is equal to the other number. It is just the opposite of the exponent function.
The equation is given as
[tex](\dfrac{1}{27})^{a+ 3} = 9[/tex]
Then take log on both sides, then we have
[tex]\rm log(\dfrac{1}{27})^{a+ 3} = log9[/tex]
We know that log aⁿ = n × log a, then we have
[tex]\rm (a+3 )log(\dfrac{1}{27}) = log9[/tex]
on simplifying, we have
a + 3 = -0.67
a = - 3 - 0.67
a = -3.67
Thus, the value of a is negative 3.67.
More about the logarithm link is given below.
https://brainly.com/question/7302008
