How to express e to the power of ln?
Answer: e to the power of ln can be written as eln(x) = x.
Let us proceed step by step.
Let us consider y = eln(x)
On applying ln to both sides we get,
ln (y) = ln eln(x)-----(1)
By using the log rule we can write ln ex = x ln(e)
ln (y) = ln (x) ln (e) [ solving RHS of equation 1 and LHS remains same]
ln (y) = ln (x) [ ln (e) = 1 ]
y will be equal to x as logs with same base are equal.
As we know from our assumption that y = eln(x)
Therefore, e to the power of ln can be written as eln(x) = x.