Question

help slove
2ln 3x +1 = 5

Answer 1

First do what is necessary to get the natural log term alone.

Answer 2

i.e. INVERSE OPERATIONS

Answer 3

1) Subtract 1 from both sides.

Answer 4

2) Divide by 2 on both sides.

Answer 5

Now you'll have:\[\ln (3x) = 2\]

Answer 6

Convert to exponent form:
\[\ln _{e}(3x) = 2 {\space} converts \to {\space} e ^{2} = 3x\]

Answer 7

4) Divide both sides by 3.

Answer 8

\[x={e ^{2} \over 3}\]

Answer 9

what is the e

Answer 10

It's an irrational number...sorta like pi.

Answer 11

It represents the base of a natural log. Which is why I added it in the 3rd step.

Answer 12

It's understood to be next to ln without actually having to write it. Sort of like if you write:

log(x) it's understood that what is really meant is:\[\log_{10}(x) \]

Answer 13

You don't have to write the 10, just like you don't have to write the e...UNLESS converting to exponent form. Which is what we did.

Answer 14

ln = natural log

Answer 15

Anyway I hope that helped. Take care and be sure to select a Best Response. Thanks

Answer 16

omg u lost me i was left with this