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For what value of a does 9 = (StartFraction 1 Over 27 EndFraction) Superscript a 3?

Sagot :

The relationship of log aⁿ = n × log a is used. Then the value of a is negative 3.67.

What is a logarithm?

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

kaydencekroner22

Answer:

a. -11/3

Step-by-step explanation:

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