Question

Which logarithmic equation is equivalent to the exponential equation below?

e5x = 6

A. ln 5x = 6
B. ln 6 = 5x
C. log 5x = 6
D. log 6 = 5x

Answer 1

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.