Answer :
To express 3125 in exponential form with base 5, let’s find an exponent [tex]\( x \)[/tex] such that:
[tex]\[ 5^x = 3125 \][/tex]
Now, let's find [tex]\( x \ step-by-step:
1. Start with the base number 5.
2. Multiply 5 by itself repeatedly until you reach the number 3125.
- \( 5^1 = 5 \)[/tex]
- [tex]\( 5^2 = 25 \)[/tex]
- [tex]\( 5^3 = 125 \)[/tex]
- [tex]\( 5^4 = 625 \)[/tex]
- [tex]\( 5^5 = 3125 \)[/tex]
We can see that [tex]\( 5^5 = 3125 \)[/tex], which means 3125 can be written as 5 raised to the power of 5.
So, the exponential form of 3125 with the base 5 is:
[tex]\[ 3125 = 5^5 \][/tex]
Therefore, the base is 5 and the exponent is 5.
[tex]\[ 5^x = 3125 \][/tex]
Now, let's find [tex]\( x \ step-by-step:
1. Start with the base number 5.
2. Multiply 5 by itself repeatedly until you reach the number 3125.
- \( 5^1 = 5 \)[/tex]
- [tex]\( 5^2 = 25 \)[/tex]
- [tex]\( 5^3 = 125 \)[/tex]
- [tex]\( 5^4 = 625 \)[/tex]
- [tex]\( 5^5 = 3125 \)[/tex]
We can see that [tex]\( 5^5 = 3125 \)[/tex], which means 3125 can be written as 5 raised to the power of 5.
So, the exponential form of 3125 with the base 5 is:
[tex]\[ 3125 = 5^5 \][/tex]
Therefore, the base is 5 and the exponent is 5.
