- #1
physicsernaw
- 41
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Why is ln(e^x) =/= x?
The domain and range of the LHS are the same as the RHS, so I don't understand why this equation is false, where e^ln(x) = x, and the LHS and RHS of this does not have the same domain...
I know that e^x and ln(x) are inverse functions, so please don't only tell me this. Why does e^ln(x) = x, while ln(e^x) =/= x?
EDIT:
Like, I understand why sin^-1(sin(x)) =/= x, whereas sin(sin^-1(x)) = x, and this is because sin^-1(x) has a range of -pi/2 to pi/2
The domain and range of the LHS are the same as the RHS, so I don't understand why this equation is false, where e^ln(x) = x, and the LHS and RHS of this does not have the same domain...
I know that e^x and ln(x) are inverse functions, so please don't only tell me this. Why does e^ln(x) = x, while ln(e^x) =/= x?
EDIT:
Like, I understand why sin^-1(sin(x)) =/= x, whereas sin(sin^-1(x)) = x, and this is because sin^-1(x) has a range of -pi/2 to pi/2
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