To find the value of [tex]\( x \)[/tex] given that the point [tex]\( (x, \frac{1}{100}) \)[/tex] lies on the graph [tex]\( y = 10^x \)[/tex], follow these steps:
1. Substitute the known point into the equation:
The point given is [tex]\( (x, \frac{1}{100}) \)[/tex].
Substitute [tex]\( y \)[/tex] with [tex]\( \frac{1}{100} \)[/tex] in the equation [tex]\( y = 10^x \)[/tex]:
[tex]\[
\frac{1}{100} = 10^x
\][/tex]
2. Express [tex]\( \frac{1}{100} \)[/tex] as a power of 10:
We know that [tex]\( \frac{1}{100} \)[/tex] can be written as [tex]\( 10^{-2} \)[/tex] because 100 is [tex]\( 10^2 \)[/tex] and taking the reciprocal gives [tex]\( 10^{-2} \)[/tex]:
[tex]\[
10^{-2} = 10^x
\][/tex]
3. Compare the exponents:
Since the bases are the same, we can equate the exponents:
[tex]\[
-2 = x
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( y = 10^x \)[/tex] given the point [tex]\( (x, \frac{1}{100}) \)[/tex] is:
[tex]\[
x = -2
\][/tex]
The answer is [tex]\( -2 \)[/tex].
