Question

Help please!!

Solve ln(5x + 7) = 8. Round to the nearest thousandth.

Answer 1

ok

Answer 2

just a sec

Answer 3

here is a trick for you:
\(\large\color{black}{ \ln(5x+7)=8 }\)
\(\large\color{black}{ \ln(5x+7)=8 \ln(e) }\)
\(\large\color{black}{ \ln(5x+7)=\ln(e^8) }\)
\(\large\color{black}{ 5x+7=e^8 }\) and on....

Answer 4

see what I did?

Answer 5

Let 5x+7=a
ln(a)=8
Find a.

Answer 6

or you could have just applied:
\(\large\color{black}{ \log_ab=c\rightarrow a^c=b }\)

Answer 7

\(\large\color{black}{ \log_ab=c~~~~~~~~~~~~~~~~\rightarrow~~~a^c=b }\)
\(\large\color{black}{ \log_e(5x+7)=8~~~\rightarrow~~~e^8=5x+7 }\)

Answer 8

subtract 7 from both sides, and divide both sides by 5.
that will be the exact solution.

Answer 9

e^8=a
a=2.079

Answer 10

And afterwards, you can approximate it, as you are told to.

Answer 11

if I lost you, tell me where please.

Answer 12

5x+7=2.079
5x=-4.921
x~~-0.984

Answer 13

Sorta lost me at log a b

Answer 14

Do you understand this rule?

\(\large\color{black}{ \log_ab=c~~~~~~\Longrightarrow~~~~~a^c=b }\)

Answer 15

without any reasons why, do you see what is going on in there?

Answer 16

I'll color it, so you can better see.

Answer 17

log 5x^7 = 8?

Answer 18

\(\Large\color{black}{ \log_{\color{red}{a}}\color{green}{b}=\color{blue}{c}~~~~~~\Longrightarrow~~~~~\color{red}{a}^\color{blue}{c}=\color{green}{b} }\)

Answer 19

you had:

\(\Large\color{black}{ \ln{}\color{green}{(5x+7)}=\color{blue}{8} }\)
which is same as,

\(\Large\color{black}{ \log_{\color{red}{e}}\color{green}{(5x+7)}=\color{blue}{8} }\)

Answer 20

apply the rule, now, what do you get?

Answer 21

if you feel you don't get something, please ask. or if you want time to process, then don't even have to reply. take your time.

Answer 22

I'm sorry about this, I'm just really bad with algebra :/
Um, e^8 = 5x + 7... and then just subtract 7 and divide 5 like you said earlier... -7/5 + e^8 = x ?

Answer 23

okay, lets do this one together:
\(\large\color{black}{ e^8=5x+7 }\)
subtracting 7 from both sides (this is to isolate the 5x)
\(\large\color{black}{ e^8\color{red}{-7}=5x+7\color{red}{-7} }\)
the \(\large\color{black}{ 7 }\)s on the rigth side cancel.
\(\large\color{black}{ e^8-7=5x }\)

Answer 24

then divide both sides by 5... (try it, even if you feel uncomfortable doing that)

Answer 25

\[\frac{ 5 }{ e^8 }-\frac{ 7 }{ 5 }=x\]

Answer 26

or the e^8 on top :P

Answer 27

it is \(\large\color{black}{ e^8 }\) over \(\large\color{black}{5 }\). like you just said, or asked, not sure about the intonation in that phrase.

Answer 28

-1.4 as a decimal for -7/5. I don't know if that would help any..

Answer 29

My connection was murdered

Answer 30

Hm?

Answer 31

Here. http://www.wolframalpha.com/input/?i=%28e%5E8%2F5%29-%287%2F5%29

note, how I put in the question/search, and how wolfram correctly interprets the input for me.

and there is a "Decimal Approximation" it is right after the "Input", right below.

Answer 32

if you have any question, ask....