Question

use natural log to solve 6e^(4x) -2=3

Answer 1

@zepdrix could you help?

Answer 2

So let's try to isolate the exponential e^(stuff) before applying any log business. Do you understand how to apply those steps? :)
How to isolate the e^(stuff)

Answer 3

nope

Answer 4

\(\large\rm 6e^{4x}-2=3\)
To undo the subtraction, we'll add 2 to each side,
\(\large\rm 6e^{4x}=5\)
To undo the 6 multiplying, we'll divide both sides by 6, ya?

Answer 5

okay, next?

Answer 6

So we have,\[\large\rm e^{4x}=\frac56\]

Answer 7

Now that our exponential is isolated (alone),
we can apply our natural log to each side,
which will hopefully help us get the x out of the exponent position like it did in the previous problem.

Answer 8

\[\large\rm \ln\left(e^{4x}\right)=\ln\left(\frac56\right)\]

Answer 9

Remember the rule that will help us here?

Answer 10

is it something to do with taking the ^4x out of the ln?
4xln e=ln(5/6)

Answer 11

Mmmm ok good. The 4x comes down in front of the log.\[\large\rm 4x \ln e=\ln\left(\frac56\right)\]

Answer 12

Recall that natural log is a log with base value e,\[\large\rm \ln(x)=\log_e(x)\]

Whenever the `base of the log` matches the `contents(argument) of the log`,
then it simplifies to 1.

Example: \(\large\rm log_4(4)=1\)

Do you see how this will help us clean up the left side of our equation?

Answer 13

yes, so lne=1

Answer 14

\[\large\rm 4x=\ln\left(\frac56\right)\]k great.

Answer 15

divide ln(5/6) by 4?

Answer 16

Mmm good good good,
that will be your final step!

Answer 17

-.046?

Answer 18

Yay good job!

Answer 19

awesome!!! thankyou sooo much!
do you mind answering a few more questions? its for a final review worksheet. its okay if you dont want to

Answer 20

lets try another one :)
I might need a break after that

Answer 21

these are some that its okay if you don't understand if you do could we do one?
use a table to solve 6^4x =63
rewrite y= square root 9x-36 =4 to make it easy to graph using a translation

Answer 22

So we're going to choose some x values,
and try to end up with 63.

Let's start with x=2 how bout.
What do you get for 6^(4x)?

Answer 23

1679616

Answer 24

Ahhh ok so we need a much much much smaller x value then ^^
my bad.

It's going to be smaller than 1 even.