Question

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

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

Answer 1

Answer:

$f(x)=log_ex$

Step-by-step 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.

Answer 2

Answer:

$f(x) = log_e(x)$

Step-by-step 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 $f(x) = lnx$