Question

If $$8^{x+1}$$ = 64 , what is the value of $$3^{2x+1}$$ ?

Options

• 1

• 3

• 9

• 27

Answer 1

We have to find the value of  ${\displaystyle 3^{2}x+1}$ provided ${\displaystyle 8^{(x+1)=64}}$

So,

 ${\displaystyle 2^{3(x+1)}=64}$

${\displaystyle 2^{3x+3}=2^6}$

Equating the exponents we get

${\displaystyle 3x+3=6}$

${\displaystyle 3x=6-3}$

${\displaystyle 3x=3}$

${\displaystyle x=\frac{3}{3}}$

 x - 1

By substitute in  ${\displaystyle 3^{2x+1}}$we get 

${\displaystyle 3^{2\times 1+1}}$

${\displaystyle =3^{2+1}}$

${\displaystyle =3^3}$

${\displaystyle =27}$

The real value of ${\displaystyle 3^{2x+1}}$ is 27