Answer :
To solve the problem of finding [tex]\( H(m-2) \)[/tex] given the expression [tex]\( 5^m = 3125 \)[/tex], let's break it down step-by-step:
1. Equation Setup: We start with the equation [tex]\( 5^m = 3125 \)[/tex]. Our goal is to find the value of [tex]\( m \)[/tex].
2. Solving for [tex]\( m \)[/tex]: We need to figure out what power of 5 gives us 3125. This involves recognizing the form of 3125:
- We see that [tex]\( 3125 = 5^5 \)[/tex] because [tex]\( 5 \times 5 \times 5 \times 5 \times 5 = 3125 \)[/tex].
3. Determining [tex]\( m \)[/tex]: Since we found that [tex]\( 3125 = 5^5 \)[/tex], it implies that [tex]\( m = 5 \)[/tex].
4. Finding [tex]\( H(m-2) \)[/tex]: With [tex]\( m = 5 \)[/tex], we compute [tex]\( m-2 \)[/tex], which is [tex]\( 5-2 = 3 \)[/tex].
5. Function [tex]\( H \)[/tex]: After calculating [tex]\( m-2 \)[/tex], we apply it to the function [tex]\( H \)[/tex]. Here, [tex]\( H(x) \)[/tex] is assumed to be an identity function, which means it simply returns the same value it was given. So, [tex]\( H(3) = 3 \)[/tex].
Therefore, the value of [tex]\( H(m-2) \)[/tex] is 3.
1. Equation Setup: We start with the equation [tex]\( 5^m = 3125 \)[/tex]. Our goal is to find the value of [tex]\( m \)[/tex].
2. Solving for [tex]\( m \)[/tex]: We need to figure out what power of 5 gives us 3125. This involves recognizing the form of 3125:
- We see that [tex]\( 3125 = 5^5 \)[/tex] because [tex]\( 5 \times 5 \times 5 \times 5 \times 5 = 3125 \)[/tex].
3. Determining [tex]\( m \)[/tex]: Since we found that [tex]\( 3125 = 5^5 \)[/tex], it implies that [tex]\( m = 5 \)[/tex].
4. Finding [tex]\( H(m-2) \)[/tex]: With [tex]\( m = 5 \)[/tex], we compute [tex]\( m-2 \)[/tex], which is [tex]\( 5-2 = 3 \)[/tex].
5. Function [tex]\( H \)[/tex]: After calculating [tex]\( m-2 \)[/tex], we apply it to the function [tex]\( H \)[/tex]. Here, [tex]\( H(x) \)[/tex] is assumed to be an identity function, which means it simply returns the same value it was given. So, [tex]\( H(3) = 3 \)[/tex].
Therefore, the value of [tex]\( H(m-2) \)[/tex] is 3.
