Question
If $(2^3)^2 = 4^x,$ then $3^x =$
✓
Answer
We have to find the value of $3^x$ provided $(2^3)^2 = 4^x$
So,
$2^{3\times 2} = 2^{2x}$
$2^6= 2^{2x}$
By equating the exponents we get
$6 = 2x$
$\frac{6}{2}=\text{x}$
$3 = x$
By substituting in $3^x $ we get
$3^x = 3^3$
$= 27$
The value of $3^x$ is $27$
So,
$2^{3\times 2} = 2^{2x}$
$2^6= 2^{2x}$
By equating the exponents we get
$6 = 2x$
$\frac{6}{2}=\text{x}$
$3 = x$
By substituting in $3^x $ we get
$3^x = 3^3$
$= 27$
The value of $3^x$ is $27$
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