1 Answer

Avshalom · Answer 1 · 2021-07-12T03:14:07+0000

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

Step-by-step 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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