Question

please, help me with this solve each exponential equation s:1.) e^x-2 = e^3x+1
2.) 7 = 6 + e^3-2x

Answer 1

\[e\large^x-2=e^{3x}+1\] or \[\large e^{x-2}=e^{3x}+1\]?

Answer 2

lol, i guess
e^(x-2) = e^(3x+1)

Answer 3

oh

Answer 4

in that case i can do it

Answer 5

please. thankyou so much

Answer 6

which one is it? there is some ambiguity here

Answer 7

so, we just compare the exponents of 'e'
e^(x-2) = e^(3x+1)
so,
x-2 = 3x+1
can you find x from here ?

Answer 8

lets assume the easiest one ;)

Answer 9

yes, i end up solving there.

Answer 10

is the second one
\[\large 7=6+e^{3-2x}\]?

Answer 11

yep

Answer 12

if so, subtract \(6\) and get
\[e^{3-2x}=1\] making
\[3-2x=0\]solve for \(x\)

Answer 13

oh, okayy thanks! i got it

Answer 14

since you are new here
\(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)

Answer 15

Thankyou! :)

Answer 16

why 3 - 2x = 0?

Answer 17

\(e^0 = 1 \\ e^{3-2x}=1 \\ 3-2x = 0\)

Answer 18

infact (anything except 0)^0 =1

Answer 19

Ah, okayy Thanks! how about this one? (5/2)^x = 4/25

Answer 20

please, if it's okay

Answer 21

i still find it hard

Answer 22

hey, no problem at all :)

Answer 23

4/25 = ...?
can you express 4 and 25 as powers of 2 and 5 ?

Answer 24

2^2

Answer 25

5^5

Answer 26

so, 4/25 = (2/5)^2
agree ?

Answer 27

5^5 ? O.o

Answer 28

ayy, joke haha/ it's 5^2!

Answer 29

^_^

Answer 30

yes,
so (2/5)^2
but we have (5/2)^x on left
so,

Answer 31

\(\Huge (\dfrac{2}{5})^2 = \dfrac{1}{(\dfrac{5}{2})^2}= (\dfrac{5}{2})^{-2}\)

got this ?

Answer 32

there ?

Answer 33

are you already a professor?

Answer 34

Thanks. gonna take note with this

Answer 35

i am a student just like you ^_^

Answer 36

and could you find x there ?

Answer 37

what year are you in?

Answer 38

wait a minute

Answer 39

i already completed my studies :)

Answer 40

so ,the x on the first problem is -3/2? and the x on my second problem would be -2. ? is my answer correct?

Answer 41

heyy heyy

Answer 42

for 2nd problem.
3-2x = 0
right ?
x = 3/2

Answer 43

ok

Answer 44

for my question e^(x-2) = e^(3x+1) we end up at x -2 = 3x+1 , can u explain to me how we come up the answer of 1.5?

Answer 45

its -1.5
x -2 = 3x+1
-2 = 2x +1
-2-1 = 2x
2x = -3
x=-3/2 = -1.5

Answer 46

ah, okay. really big thanks! is it really okay, i still have more questions

Answer 47

:)

Answer 48

i'll be glad to help :)