If ln(a) = ln(b). Is that mean a=b?

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Answer 1 · 2017-10-29T11:37:34

Yes, $a = b$ $a=b$ $[a and b > 0]$ $[a and b >0]$

$ln a = ln b$ $lna = lnb$

Clearly ${a and b} > 0$ ${a and b} >0$ for this equation to be valid.

Raise $e$ $e$ to the power of each side of the equation.

$e^{ln a} = e^{ln b}$ $e^(lna) = e^(lnb)$

Remember that $e^{ln x} = x$ $e^lnx = x$

Thus: $e^{ln a} = a$ $e^(lna) = a$

and

$e^{ln b} = b$ $e^(lnb) =b$

Hence, $a = b$ $a=b$