Question

Simplify: e^(1+lnx)

Answer 1

When you have a sum of exponents you can break it into a product of powers of the base:
\[\large e^{1+ln(x)} = e^1 \cdot e^{ln(x)}\]

Answer 2

ex

e^1 = e
e^(ln(x)) = x
e*x = ex

Answer 3

Now then by the laws of logs: \[\large b^{log_b(a)} = a\]Therefore \[e^{ln(x)} = x\]

Answer 4

And \(e^1= e\)

So \[\large e^{1+ln(x)} = e^1 \cdot e^{ln(x)} = e\cdot x = ex\]

Answer 5

So it's simplified just down to ex?