Question

Use natural logarithms to solve the equation. Round to the nearest thousandth.
6e4x - 2 = 3

A. –0.448

B. 0.327

C. 0.067

D. –0.046

Answer 1

what is the e thing, also show work so i can understand

Answer 2

@jim_thompson5910

Answer 3

@JakeV8

Answer 4

\[\Large 6e^{4x}-2=3\] ???

Answer 5

yes

Answer 6

Start off by adding 2 to both sides

Answer 7

\[6e ^{4x}=5\]

Answer 8

now divide both sides by 6

Answer 9

\[e ^{4x}= .8333333333\]

Answer 10

then convert to logarithmic form

Answer 11

this gives you

4x = ln(0.833333333)

Answer 12

the next thing to do is evaluate the right side

finally, divide both sides by 4 and round

Answer 13

no im confused i dont know how to put this in my calculator

Answer 14

there is an "ln" button (LN)

Answer 15

nope

Answer 16

probably near the Log button

Answer 17

what kind of calculator do you have

Answer 18

TI-84

Answer 19

under the log button is the LN button

Answer 20

type LN, then enter 0.8333333 and hit enter

Answer 21

not on mine its sto

Answer 22

weird, guess I'm looking at the wrong version?

Answer 23

o i found it

Answer 24

-.1823215969

Answer 25

now divide that by 4

Answer 26

-.0455803992

Answer 27

then round to 3 decimal places

Answer 28

-0.046??

Answer 29

good

Answer 30

Another way to do it

\[\Large 6e^{4x}-2=3\]

\[\Large 6e^{4x}=3+2\]

\[\Large 6e^{4x}=5\]

\[\Large e^{4x}=\frac{5}{6}\]

\[\Large 4x=\ln\left(\frac{5}{6}\right)\]

\[\Large 4x\approx-0.18232155679\]

\[\Large x\approx\frac{-0.18232155679}{4}\]

\[\Large x\approx-0.045580389\]

\[\Large x\approx-0.046\]

Answer 31

thanks you for your help

Answer 32

oh wait, nvm, I'm thinking of something else...but what I showed just now is what you just did

Answer 33

o so im wrong

Answer 34

no you are 100% correct

Answer 35

o ok lol

Answer 36

I just thought my steps were different from yours (when they aren't really)