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

- anonymous

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

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- anonymous

The problem is
2^x+3=5x

- anonymous

What did you get?

- anonymous

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

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## More answers

- anonymous

I got 2.269

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

no 2^ x+3=5x

- anonymous

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

- anonymous

Which is gonna be a pain.

- anonymous

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

- anonymous

Yes

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Ok good.

- anonymous

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

- anonymous

Then solve for x. Don't plug anything into your calculator until you have something where
x = something that has no x

- anonymous

(x+3)ln2=xln5
is correct for starting out

- anonymous

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

- anonymous

Get all terms with an x on one side.

- anonymous

Or that. Cross multiplying works fine

- anonymous

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

- anonymous

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

- anonymous

Not just the 3.

- anonymous

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

- anonymous

then:
x+3=2.322x

- anonymous

Don't plug things in.

- anonymous

Keep solving the equation until you have x by itself.
x = something that has no x.

- anonymous

Then plug in

- anonymous

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

- anonymous

I think cross multiplying is just making this harder.

- anonymous

I just got a different answer of -4.425

- anonymous

Lets back up.

- anonymous

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

- anonymous

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

- anonymous

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.

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