Answer :
Sure! Let's rewrite the given equation in logarithmic form step by step.
We are given the exponential equation:
[tex]\[ 14^2 = 196 \][/tex]
To convert an exponential equation to its logarithmic form, we need to use the definition of logarithms. The definition of a logarithm is:
[tex]\[ \log_b(a) = c \][/tex]
This means "the logarithm of [tex]\( a \)[/tex] with base [tex]\( b \)[/tex] is [tex]\( c \)[/tex]" if and only if:
[tex]\[ b^c = a \][/tex]
Now, let's apply this to our given equation [tex]\( 14^2 = 196 \)[/tex]:
- Here, the base [tex]\( b \)[/tex] is [tex]\( 14 \)[/tex].
- The exponent [tex]\( c \)[/tex] is [tex]\( 2 \)[/tex].
- The result [tex]\( a \)[/tex] is [tex]\( 196 \)[/tex].
So, following the definition:
[tex]\[ \log_{14}(196) = 2 \][/tex]
Therefore, the correct logarithmic form of the given equation [tex]\( 14^2 = 196 \)[/tex] is:
[tex]\[ \log_{14}(196) = 2 \][/tex]
Now, let's match this with the given options:
A) [tex]\(\log_{14}(196) = 2\)[/tex]
B) [tex]\(\log_{196}(2) = 14\)[/tex]
C) [tex]\(\log_{2}(196) = 14\)[/tex]
D) [tex]\(\log_{14}(2) = 196\)[/tex]
The correct answer is:
A) [tex]\(\log_{14}(196) = 2\)[/tex]
We are given the exponential equation:
[tex]\[ 14^2 = 196 \][/tex]
To convert an exponential equation to its logarithmic form, we need to use the definition of logarithms. The definition of a logarithm is:
[tex]\[ \log_b(a) = c \][/tex]
This means "the logarithm of [tex]\( a \)[/tex] with base [tex]\( b \)[/tex] is [tex]\( c \)[/tex]" if and only if:
[tex]\[ b^c = a \][/tex]
Now, let's apply this to our given equation [tex]\( 14^2 = 196 \)[/tex]:
- Here, the base [tex]\( b \)[/tex] is [tex]\( 14 \)[/tex].
- The exponent [tex]\( c \)[/tex] is [tex]\( 2 \)[/tex].
- The result [tex]\( a \)[/tex] is [tex]\( 196 \)[/tex].
So, following the definition:
[tex]\[ \log_{14}(196) = 2 \][/tex]
Therefore, the correct logarithmic form of the given equation [tex]\( 14^2 = 196 \)[/tex] is:
[tex]\[ \log_{14}(196) = 2 \][/tex]
Now, let's match this with the given options:
A) [tex]\(\log_{14}(196) = 2\)[/tex]
B) [tex]\(\log_{196}(2) = 14\)[/tex]
C) [tex]\(\log_{2}(196) = 14\)[/tex]
D) [tex]\(\log_{14}(2) = 196\)[/tex]
The correct answer is:
A) [tex]\(\log_{14}(196) = 2\)[/tex]
