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C3 functions

e^{ln(a)}=a

how does this works?

i don't understand why e to the natural log of something is just someting

Reply 1

GabbytheGreek_48

im also doing core 3 but um I think I can explain its like with core 2 where you have an exponential and a log of x they just equal x

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Reply 2

nao123

well, they are inverse functions of one another so if f(x) =lnx then f^-1(x)= e^x.
and we know that f^-1(f(x)) is always x. or vice versa.

Reply 3

B_9710

They are inverses, so

e^{\ln x}=\ln e^x =x

.
Alternatively you can think of it this way. lna is the number that you need to raise e by to get a, so for

e^{ \ln a}

you are then raising e by this power, so it's a.

Reply 4

bigdonger

Original post by GabbytheGreek_48

im also doing core 3 but um I think I can explain its like with core 2 where you have an exponential and a log of x they just equal x

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Original post by nao123