MCQ
If $8^{x+1} = 64$, what is the value of $3^{2x+1}?$
- A$1$
- B$3$
- C$9$
- ✓$27$
✓
Answer
Correct option: D.
$27$
We have to find the value of $3^{2 x+1}$ provided $8^{x+1}=64$
So,
$ 2^{3(x+1)}=64$
$ 2^{3 x+3}=2^6$
Equating the exponents we get
$ 3 x+3=6$
$ 3 x=6-3$
$ 3 x=3$
$x=\frac{3}{3}$
$ x=1$
By substitute in $3^{2 \mathrm{x}+1}$ we get
$ =3^{2 \times 1+1} $
$ =3^{2+1} $
$ =3^3 $
$ =27$
The real value of $3^{2 x+1}$ is $27$
Hence the correct choice is $d.$
So,
$ 2^{3(x+1)}=64$
$ 2^{3 x+3}=2^6$
Equating the exponents we get
$ 3 x+3=6$
$ 3 x=6-3$
$ 3 x=3$
$x=\frac{3}{3}$
$ x=1$
By substitute in $3^{2 \mathrm{x}+1}$ we get
$ =3^{2 \times 1+1} $
$ =3^{2+1} $
$ =3^3 $
$ =27$
The real value of $3^{2 x+1}$ is $27$
Hence the correct choice is $d.$
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