Question

How would you simplify e^x+ln3 ?

Answer 1

Guide me please, no direct answers

Answer 2

e^(x+ln3)

Answer 3

Sorry this is easy

Answer 4

remember the rule,

A^(b + c) = A^bA^c

Answer 5

The answer is 3e^x

Wondering how this was derived.

Answer 6

Also remember the rule

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

Answer 7

One more rule you need to remember

ln(x^a) = aln(x)

Answer 8

Can you solve it now?

Answer 9

Sorry I'm pretty exhausted can't believe I spaced on this

Answer 10

hehe

Answer 11

Not really.. The x is confusing me

Answer 12

\(\bf \Large{ e^{x+ln(3)}\implies e^{x+log_e(3)}\implies e^x\cdot e^{log_e(3)}\\ \quad \\
\textit{log cancellation rule of } {\color{red}{ a}}^{log_{\color{red}{ a}}x}=x\quad thus\\ \quad \\

e^x\cdot {\color{red}{ e}}^{log_{\color{red}{ e}}(3)}\implies e^x\cdot \square ?}\)

Answer 13

Still don't understand it. Will need to watch a video again. I hate logs.

Answer 14

Logs are easy, just look at the rules I posted

Answer 15

heeh lemme rewrite the rule withuot the "x"

Answer 16

Dont get frustrated you can do this :)

Answer 17

\(\bf \Large{ e^{x+ln(3)}\implies e^{x+log_e(3)}\implies e^x\cdot e^{log_e(3)}\\ \quad \\
\textit{log cancellation rule of } {\color{red}{ a}}^{log_{\color{red}{ a}}\square }=\square \quad thus\\ \quad \\

e^x\cdot {\color{red}{ e}}^{log_{\color{red}{ e}}(3)}\implies e^x\cdot \square ?}\)

Answer 18

Ok so the ln^3 becomes = 3
And we are left with the e^x
So 3e^x
Is that all?

Answer 19

yeap

Answer 20

Ok cool thanks you guys will need some more practice!

Answer 21

yw

Answer 22

@intraining:
Part of the difficulty with this problem stems from the ambiguity in e^x + ln 3.
If one were to take this expression literally, and graph the result, the graph would look lik3e that of y=e^x shifted upward by the constant quantity ln 3.

On second thought, it occurred to me that you meant e^(x+ln 3). This is an entirely different problem.

Since
\[e ^{a+b}=e ^{a}e ^{b}\]

\[e ^{x+\ln 3}=e ^{x}e ^{\ln 3}=3e ^{x}\]

When in doubt, please use parentheses!

Answer 23

Thank you mathmale!

Answer 24

My great pleasure!!