Question

How do you solve the function ;;

10=1.5e^x
and
6e^2x=7e^4x

Answer 1

for the first one, divide both sides by and take the natural log of both sides

Answer 2

*divide both sides by 1.5

Answer 3

@Vocaloid okay I was doing that, and got to In 6.66 = e^x

Answer 4

good, now take the natural log

ln(6.66) = x

Answer 5

x = about 1.9

Answer 6

good

Answer 7

For \[6e^{2x}=7e^{4x}\]
How do you start that? I am getting these, I just iddn't know what you did with variables on each side

Answer 8

taking the natural log cancels out the e

Answer 9

ln(e^x) = x

Answer 10

Oh.. so it would be In(6)=In(7) basically, to get rid of the 'e' then bring down the exponents to be leading coeffications in front of the natural logs?

Answer 11

not quite

Answer 12

first we can divide both sides by 6, like so:

Answer 13

then we can rewrite e^4x as (e^2x)*(e^2x) via the exponent rule

Answer 14

Would that cancel out the e^2x and leave one side with an e^2x or am I going the wrong way with that?

Answer 15

yeah, you're right

Answer 16

So 1 = 7/6(e^2x)?

Answer 17

yeah, then we divide both sides by (7/6)

Answer 18

then we take the natural log of both sides

Answer 19

x= (about) -0.077

Answer 20

great. is anything still unclear?

Answer 21

No. It makes sense now. The first one I had the answer, I doubted myself. The second one, I see now. I didn't know how to get it into a simplified form to solve. Thank you so much @Vocaloid !!