Answer :
To express 3125 in exponential form with base 5, we need to find a number such that [tex]\( 5 \)[/tex] raised to the power of that number equals 3125. Here's a step-by-step solution to achieve that:
1. Understand the problem: We need to express 3125 as [tex]\( 5^x \)[/tex], where [tex]\( x \)[/tex] is an exponent. Specifically, we are searching for the exponent [tex]\( x \)[/tex] that satisfies the equation.
2. Start with the base number: The base given in the problem is 5. We need to see how many times we can multiply 5 by itself to get 3125.
3. Perform exponentiation until you reach 3125:
- [tex]\( 5^1 = 5 \)[/tex]
- [tex]\( 5^2 = 25 \)[/tex]
- [tex]\( 5^3 = 125 \)[/tex]
- [tex]\( 5^4 = 625 \)[/tex]
- [tex]\( 5^5 = 3125 \)[/tex]
4. Identify the exponent: By listing these calculations, we see that [tex]\( 5^5 \)[/tex] equals 3125.
Therefore, 3125 in exponential form with base 5 is:
[tex]\[ 5^5 \][/tex]
So, the exponential form of 3125 with base 5 is [tex]\( 5^5 \)[/tex].
1. Understand the problem: We need to express 3125 as [tex]\( 5^x \)[/tex], where [tex]\( x \)[/tex] is an exponent. Specifically, we are searching for the exponent [tex]\( x \)[/tex] that satisfies the equation.
2. Start with the base number: The base given in the problem is 5. We need to see how many times we can multiply 5 by itself to get 3125.
3. Perform exponentiation until you reach 3125:
- [tex]\( 5^1 = 5 \)[/tex]
- [tex]\( 5^2 = 25 \)[/tex]
- [tex]\( 5^3 = 125 \)[/tex]
- [tex]\( 5^4 = 625 \)[/tex]
- [tex]\( 5^5 = 3125 \)[/tex]
4. Identify the exponent: By listing these calculations, we see that [tex]\( 5^5 \)[/tex] equals 3125.
Therefore, 3125 in exponential form with base 5 is:
[tex]\[ 5^5 \][/tex]
So, the exponential form of 3125 with base 5 is [tex]\( 5^5 \)[/tex].
