For what value of x satisfy the given equation: 3ˣ = 81 ? * 2 points a) 0 b) 4 c) 1 d) 3 About the author Evelyn
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 Reply
Answer:
c ) 3
Step-by-step explanation:
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