Question

How does e^(ln3)=3?

Answer 1

\(a^{\log_a(x)}=x\)

Answer 2

omg yes! i remember this now! how would that apply to e^(2ln5)

Answer 3

By definition we have

\(\large y=\log_a(x) \implies a^y=x\)

so if we substitute in for y, we get

\(\large x = a^y=a^{log_a(x)}\)

Answer 4

we also have this property

\[\log(x^y)=y\log(x)\]
so

\[e^{2\ln(5) }=e^{\ln(2^5)}=2^5 = 32\]

Answer 5

wouldn't it be \[e ^{\ln(5^{2)}}\] ?

Answer 6

yeah sorry

Answer 7

so 5^2 = 25

Answer 8

ahh ok i see it now :)

Answer 9

\(e^{2\ln(5) }=e^{\ln(5^2)}=5^2 = 25\)

Answer 10

long day....

Answer 11

its fine! I understood :)

Answer 12

I appreciate your help!

Answer 13

np