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Andreyy89
3 years ago
10

Which logarithmic equation is equivalent to the exponential equation below?

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
7 0

Option B: \ln 6=5 x is the correct answer.

Explanation:

The exponential equation is e^{5 x}=6

If f(x)=g(x), then \ln (f(x))=\ln (g(x))

Thus, the equation becomes

\ln \left(e^{5 x}\right)=\ln (6)

Applying log rule, \log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x) and thus the equation becomes

5 x \ln (e)=\ln (6)

Since, we know that, \ln (e)=1, using this we get,

5 x=\ln (6)

Hence, the logarithmic equation which is equivalent to the exponential equation e^{5 x}=6 is \ln 6=5 x

Thus, Option B is the correct answer.

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