Question

I need someone to just check my work... and tell me where I went wrong?

Answer 1

The problem is
2^x+3=5x

Answer 2

What did you get?

Answer 3

next step:
(x+3)ln2/xln2=xln5/xln2

Answer 4

I got 2.269

Answer 5

next step:
x+3/x=ln5/ln2

Answer 6

next step:
x+3/x=2.322/1

Answer 7

Something is wrong. Was the original equation
\[2^{x+3} = 5^x\]
?

Answer 8

no 2^ x+3=5x

Answer 9

Ok, then when you take the ln of both sides you'll have ln5 + lnx on the right hand side of the equal.

Answer 10

Which is gonna be a pain.

Answer 11

Was it \[2^{x+3} = 5x\] ?

Answer 12

Yes

Answer 13

Yeah, there's no good way to simplify that. I suspect you have the question wrong.

Answer 14

Best you can do is something like
\[x(ln 2) - lnx = ln(5/3)\]

Answer 15

Err wait, that should be ln(5/8) on the right side.

Answer 16

My teacher told us to set each side to the natural...
which gave me:
(x+3)ln2=xln5

Answer 17

Then I needed to get everything canceled out by cross multiplying... so I divided both sides by xln2

Answer 18

That's not right though. Unless you had 5^x on the right side originally.

Answer 19

Was it \(5x\) or \(5^x\)

Answer 20

the second one... I just looked in my book. Im so sorry

Answer 21

Ok good.

Answer 22

So yeah that's right. take the ln of both sides (or any log really)

Answer 23

Then solve for x. Don't plug anything into your calculator until you have something where

x = something that has no x

Answer 24

(x+3)ln2=xln5

is correct for starting out

Answer 25

ok... then what do I need to divide both sides by? she taught us to cross multiply? I divided both sides by xln2 just to cancel out. And I ended up with
x+3/x=ln5/ln2

Answer 26

Get all terms with an x on one side.

Answer 27

Or that. Cross multiplying works fine

Answer 28

I usually multiply out products, but you don't need to here

Answer 29

Just be sure that you do (x+3)/x = ln5/ln2

Answer 30

Not just the 3.

Answer 31

I did and I got:
x+3/x= 2.322/1

Answer 32

then:
x+3=2.322x

Answer 33

Don't plug things in.

Answer 34

Keep solving the equation until you have x by itself.

x = something that has no x.

Answer 35

Then plug in

Answer 36

Im not sure what/where.I am attempting to get x by itself? I thought that is what I was doing?

Answer 37

I think cross multiplying is just making this harder.

Answer 38

I just got a different answer of -4.425

Answer 39

Lets back up.

Answer 40

Ok..Im just trying to follow the instructions. But Im willing to try anything at this point

Answer 41

\[(x+3)ln2=xln5\]
\[x(ln2)+3(ln2)=x(ln5)\]
\[x(ln2)- x(ln5)= - 3(ln2)\]
\[x[(ln2)- (ln5)]= - 3(ln2)\]
\[x= \frac{- 3(ln2)}{(ln2)- (ln5)}\]

Answer 42

Thanks for your time.. I appreciate it. I will continue to search for the answer. I need to learn it the way she taught us, Im afraid I will be jumping the gun and not learning anything... thanks so much.