For what value of x satisfy the given equation: 3ˣ = 81 ? *
2 points
a) 0
b) 4
c) 1
d) 3

Answer:

Correct option is

A

2

Let 81

sin

2

x

=y

81

cos

2

x

=81

1−sin

2

x

=81y

−1

So that the given equation can be written as

y

2

−30y+81=0⇒y=3 or y=27

⇒81

sin

2

x

=3 or 27

⇒3

4sin

2

x

=3

1

or 3

3

⇒4sin

2

x=1 or 3

⇒sin

2

x=

4

1

or

4

3

⇒sinx=±

2

1

or ±

2

3

⇒x=

6

π

,

3

π

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