Question

3^x-2 = 4^2x+4 can you solve this in ln form?

Answer 1

take logs of both sides

Answer 2

wait then when do you use natural logs?

Answer 3

@Moyo30

Answer 4

In is natural log so take In of both sides

Answer 5

okay thats my first step...then what is next?

Answer 6

what do u get?

Answer 7

if you take the log of both sides?

Answer 8

i got \[(x-2)\ln3=(2x+4)\ln4\]

Answer 9

@Moyo30

Answer 10

collect like terms

Answer 11

but dont i have to convert to logs?

Answer 12

u have used the logs to get to that stage but u need to simplify further

Answer 13

okay so i got x (ln3-2ln4) = 4ln4+2ln3

Answer 14

then further simplify to solve for x

Answer 15

x=(4ln(4) + 2ln3)) / (ln(3) - 2ln(4))

Answer 16

You must learn to write more clearly. What you have written

3^x-2 = 4^2x+4

means this

\(3^{x} - 2 = \left(4^{2}\cdot x\right) + 4\)

If you mean something else, please use sufficient parentheses to clarify.

Remember that the Order of Operations ALWAYS works!

Answer 17

so i got this http://bamboodock.wacom.com/doodler/9459161b-e500-4329-9818-c0bf0d611c8a

Answer 18

so do i turn into log after this?

Answer 19

You can continue to simplfy. Use your log rules.

Answer 20

i am so lost ><

Answer 21

It does not matter if you use log or ln. In this case, it doesn't matter what base you are using. So far, you have done nothing that requires any particular base.

Answer 22

okay well why is ln and log answers are different?

Answer 23

Three possibilities come to mind:

1) They aren't.
2) It is made clear which base to use and you are looking at the wrong one.
3) You are missing something.

How shall we determine which it is?

Answer 24

ln is to log to base e (e is a special number) approximate value of e = 2.718
log is base 10

Answer 25

okay but the book gave an example of solving log equations and it was using through ln and this was the example http://bamboodock.wacom.com/doodler/e2ff45a5-3ae8-477a-9464-d3bee76dd49b so i thought you solve the equation through ln but there was another problem but the answer book said to use by log and i was lost from there

Answer 26

\(3^{x-2} = 4^{2x+4}\)

Introduce logs base 10

\((x-2)\cdot\log_{10}(3) = (2x+4)\cdot\log_{10}(4)\)

Introduce logs base e

Choose from
\((x-2)\cdot\log_{e}(3) = (2x+4)\cdot\log_{e}(4)\)
\((x-2)\cdot\ln(3) = (2x+4)\cdot\ln(4)\)
\((x-2)\cdot\log(3) = (2x+4)\cdot\log(4)\)

Introduce logs base 2

\((x-2)\cdot\log_{2}(3) = (2x+4)\cdot\log_{2}(4)\)

It does not matter, so long as the context is clear and you remain consistent.

Answer 27

OMG THANK YOU SO MUCH! this made it so clear!

Answer 28

thank you thank you thank you!!!