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Answer :
To solve the problem, let's start by understanding the given logarithmic equation: [tex]\(\log_{14} 196 = 2\)[/tex].
This equation states that 14 raised to the power of 2 equals 196. In mathematical form, it means:
[tex]\[ 14^2 = 196 \][/tex]
Let's go through the options one by one to find the statement that matches this result:
A) [tex]\(14^2 = 196\)[/tex]
- This statement is exactly what we found from the logarithmic equation. When you raise 14 to the power of 2, you get 196, which is correct.
B) [tex]\(2^{196} = 14\)[/tex]
- This suggests that raising 2 to the power of 196 equals 14, which does not relate to our initial equation and is incorrect.
C) [tex]\(14^{196} = 2\)[/tex]
- This suggests that 14 raised to the power of 196 equals 2, which is not related to our equation and is incorrect.
D) [tex]\(2^{14} = 196\)[/tex]
- This suggests that raising 2 to the power of 14 equals 196, which does not match our initial equation.
The correct choice is option A since it matches what we know from the logarithmic equation provided: [tex]\(14^2 = 196\)[/tex].
This equation states that 14 raised to the power of 2 equals 196. In mathematical form, it means:
[tex]\[ 14^2 = 196 \][/tex]
Let's go through the options one by one to find the statement that matches this result:
A) [tex]\(14^2 = 196\)[/tex]
- This statement is exactly what we found from the logarithmic equation. When you raise 14 to the power of 2, you get 196, which is correct.
B) [tex]\(2^{196} = 14\)[/tex]
- This suggests that raising 2 to the power of 196 equals 14, which does not relate to our initial equation and is incorrect.
C) [tex]\(14^{196} = 2\)[/tex]
- This suggests that 14 raised to the power of 196 equals 2, which is not related to our equation and is incorrect.
D) [tex]\(2^{14} = 196\)[/tex]
- This suggests that raising 2 to the power of 14 equals 196, which does not match our initial equation.
The correct choice is option A since it matches what we know from the logarithmic equation provided: [tex]\(14^2 = 196\)[/tex].
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