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

Question

Accepted Answer

The correct option is 3:
To solve this problem, we need to first find the value of $x$ from the given equation $8^{x+1} = 64$. Then, we will substitute the value of $x$ into the expression $3^{x+1}$ to find its value.

Step 1: Solve the exponential equation $8^{x+1} = 64$.
We know that $64$ can be expressed as a power of $8$.
$64 = 8 	imes 8 = 8^2$
So, the equation becomes:
$8^{x+1} = 8^2$
When the bases are the same in an exponential equation, the exponents must be equal.
Therefore, we can equate the exponents:
$x+1 = 2$

Step 2: Solve for $x$.
Subtract $1$ from both sides of the equation:
$x = 2 - 1$
$x = 1$

Step 3: Substitute the value of $x$ into the expression $3^{x+1}$.
Now that we have found $x=1$, we can substitute this value into the expression $3^{x+1}$.
$3^{x+1} = 3^{1+1} = 3^2$

Step 4: Calculate the final value.
$3^2 = 3 	imes 3 = 9$
So, the value of $3^{x+1}$ is $9$.

The incorrect option is 1: This option might be chosen if there was a calculation error or a misunderstanding of the exponent. For example, if $x$ was incorrectly determined or if $3^{x+1}$ was miscalculated.
The incorrect option is 2: This option is incorrect because if $3^{x+1}=3$, then $x+1=1$, which means $x=0$. However, $8^{0+1} = 8^1 = 8$, which is not equal to 64.
The incorrect option is 4: This option would be correct if $x+1$ were $0$, making $3^0=1$. However, this would mean $8^{x+1}=8^0=1$, which contradicts $8^{x+1}=64$.