If \(104_x = 68\), find the value of x
Question 1 Report
If \(104_x = 68\), find the value of x
Answer Details
To find the value of x, we need to convert the given number from base-x to base-10, and then solve for x.
First, let's write out what the given number means in expanded form:
\begin{align*}
104_x &= 1 \times x^2 + 0 \times x^1 + 4 \times x^0 \\
&= x^2 + 4
\end{align*}
We're also told that this equals 68, so we can set up an equation:
$$x^2 + 4 = 68$$
Solving for x, we get:
\begin{align*}
x^2 &= 64 \\
x &= \pm 8
\end{align*}
Since x is the base of a number system, it must be a positive integer. Therefore, the only possible solution is x = 8.
Therefore, the value of x is 8.
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