Answer :
Let's find the logarithmic form of the equation [tex]\( 25 = 5^2 \)[/tex].
### Step-by-Step Solution:
1. Identify the Base, Exponent, and Result:
- Base: The base of the exponentiation is [tex]\( 5 \)[/tex].
- Exponent: The exponent is [tex]\( 2 \)[/tex].
- Result: The result of the exponentiation is [tex]\( 25 \)[/tex].
2. Apply the Definition of Logarithms:
- A logarithm is an exponent that the base must be raised to in order to get the result.
- The general form for logarithms is:
[tex]\[ \log_b a = c \][/tex]
This reads as "logarithm of [tex]\( a \)[/tex] with base [tex]\( b \)[/tex] is [tex]\( c \)[/tex]"
3. Match Our Equation to Logarithmic Form:
- Using [tex]\( 25 = 5^2 \)[/tex]:
[tex]\[ \log_5 25 = 2 \][/tex]
4. Choose the Correct Option:
- Looking at the given choices:
1. [tex]\( \log_2 5 = 25 \)[/tex] - This is incorrect.
2. [tex]\( \log_{25} 2 = 5 \)[/tex] - This is incorrect.
3. [tex]\( \log_5 25 = 2 \)[/tex] - This is correct.
4. [tex]\( \log_5 2 = 25 \)[/tex] - This is incorrect.
Therefore, the correct logarithmic form of [tex]\( 25 = 5^2 \)[/tex] is:
[tex]\[ \log_5 25 = 2 \][/tex]
Thus, the corresponding correct choice is:
[tex]\[ 3. \log_5 25 = 2 \][/tex]
### Step-by-Step Solution:
1. Identify the Base, Exponent, and Result:
- Base: The base of the exponentiation is [tex]\( 5 \)[/tex].
- Exponent: The exponent is [tex]\( 2 \)[/tex].
- Result: The result of the exponentiation is [tex]\( 25 \)[/tex].
2. Apply the Definition of Logarithms:
- A logarithm is an exponent that the base must be raised to in order to get the result.
- The general form for logarithms is:
[tex]\[ \log_b a = c \][/tex]
This reads as "logarithm of [tex]\( a \)[/tex] with base [tex]\( b \)[/tex] is [tex]\( c \)[/tex]"
3. Match Our Equation to Logarithmic Form:
- Using [tex]\( 25 = 5^2 \)[/tex]:
[tex]\[ \log_5 25 = 2 \][/tex]
4. Choose the Correct Option:
- Looking at the given choices:
1. [tex]\( \log_2 5 = 25 \)[/tex] - This is incorrect.
2. [tex]\( \log_{25} 2 = 5 \)[/tex] - This is incorrect.
3. [tex]\( \log_5 25 = 2 \)[/tex] - This is correct.
4. [tex]\( \log_5 2 = 25 \)[/tex] - This is incorrect.
Therefore, the correct logarithmic form of [tex]\( 25 = 5^2 \)[/tex] is:
[tex]\[ \log_5 25 = 2 \][/tex]
Thus, the corresponding correct choice is:
[tex]\[ 3. \log_5 25 = 2 \][/tex]
