To determine the exponent [tex]\( ? \)[/tex] that satisfies the equation [tex]\( 10^? = 10,000 \)[/tex], let's break it down step by step.
1. The equation given is [tex]\( 10^? = 10,000 \)[/tex].
2. We know that 10,000 is a power of 10. To express 10,000 as a power of 10, we can write it in the form [tex]\( 10^k \)[/tex].
3. Recall that:
[tex]\[
10^1 = 10
\][/tex]
[tex]\[
10^2 = 100
\][/tex]
[tex]\[
10^3 = 1,000
\][/tex]
[tex]\[
10^4 = 10,000
\][/tex]
4. From this, we can see that [tex]\( 10,000 \)[/tex] is [tex]\( 10 \)[/tex] raised to the power of 4. Therefore, the exponent [tex]\( k \)[/tex] in the expression [tex]\( 10^k = 10,000 \)[/tex] is 4.
Thus, the exponent [tex]\( ? \)[/tex] that makes the equation [tex]\( 10^? = 10,000 \)[/tex] true is:
[tex]\[
? = 4
\][/tex]
