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Rewrite each equation in logarithmic form.

27) [tex]14^2=196[/tex]

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]

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]

Thanks for taking the time to read Rewrite each equation in logarithmic form 27 tex 14 2 196 tex A tex log 14 196 2 tex B tex log 196 2 14. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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