It equals ln(x), yes. Log base e of x is the same as ln(x)
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ln functions just like log, but log's standard base is 10 and ln's standard base is "e" (approx. 2.72). So you have to be taking the ln of something and in this equation ln is by itself. Which is not possible. So this is neither true or false, it's just not possible.
Hope this helped!
Edit: However, if this equation is actually equal to ln x, then it would be true.
log(e) x = ln(e) x
(ln always has base e)
So if you use what my teacher calls the circle method...
Take the base of the left side (e) and put it to the power of the entire right side of the equation (ln(e) x) and set it equal to what you are taking the log of on the left side (x).
e^ln(e) x = x
In the rules of logarithms, the e^ln(e) cancels out to leave just x on the left side.
And x = x so it is true.
Hope this helped!
Edit: However, if this equation is actually equal to ln x, then it would be true.
log(e) x = ln(e) x
(ln always has base e)
So if you use what my teacher calls the circle method...
Take the base of the left side (e) and put it to the power of the entire right side of the equation (ln(e) x) and set it equal to what you are taking the log of on the left side (x).
e^ln(e) x = x
In the rules of logarithms, the e^ln(e) cancels out to leave just x on the left side.
And x = x so it is true.
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ln is just a logarithm (log) to the power of e so yes, this statement is TRUE.
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true