Question

Which function is equivalent to f(x) = lnx?

f(x) = log3x
f(x) = log10x
f(x) = logbx
f(x) = logex

Answer 1

`f(x) = log_e(x)`

Explanation:

`f(x) = ln x`

For logarithmic function ln(x) the base of ln is 'e'

`f(x) = log_3(x)`

The base of log is 3 . so it is not equivalent to
`f(x) = lnx`

`f(x) = log_(10)(x)`

The base of log is 10 . so it is not equivalent to
`f(x) = lnx`

`f(x) = log_b(x)`

The base of log is b . so it is not equivalent to
`f(x) = lnx`

`f(x) = log_e(x)`

The base of log is e . so it is equivalent to
`f(x) = lnx`

Answer 2

`f(x)=log_ex`

Explanation:

By definition, we can write ln instead of log. WHEN??

Whenever the base of the logarithm is the number "e".

Hence, when we have:

`Log_e`

We can write it in shortcut as:

`Log_e=ln`

Hence, ln x can also be written as
`Log_ex`

Fourth answer choice is right.