MCQ
If $(2^3)^2=4^x$, then $3^x=$
- A$3$
- B$6$
- C$9$
- ✓$27$
✓
Answer
Correct option: D.
$27$
We have to find the value of $3^{\mathrm{x}}$ provided $(2^3)^2=4^{\mathrm{x}}$
So,
$2^{3 \times 2}=2^{2 x}$
$2^6=2^{2 x}$
By equating the exponents we get
$6=2 x$
$\frac{6}{2}=\text{x}$
$3=x$
By substituting in $3^{\mathrm{x}}$ we get
$3^x=3^3$
$=27$
The value of $3^{\mathrm{x}}$ is $27$
Hence the correct choice is $d$.
So,
$2^{3 \times 2}=2^{2 x}$
$2^6=2^{2 x}$
By equating the exponents we get
$6=2 x$
$\frac{6}{2}=\text{x}$
$3=x$
By substituting in $3^{\mathrm{x}}$ we get
$3^x=3^3$
$=27$
The value of $3^{\mathrm{x}}$ is $27$
Hence the correct choice is $d$.
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