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

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

Mathematics
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The problem is 2^x+3=5x
What did you get?
next step: (x+3)ln2/xln2=xln5/xln2

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I got 2.269
next step: x+3/x=ln5/ln2
next step: x+3/x=2.322/1
Something is wrong. Was the original equation \[2^{x+3} = 5^x\] ?
no 2^ x+3=5x
Ok, then when you take the ln of both sides you'll have ln5 + lnx on the right hand side of the equal.
Which is gonna be a pain.
Was it \[2^{x+3} = 5x\] ?
Yes
Yeah, there's no good way to simplify that. I suspect you have the question wrong.
Best you can do is something like \[x(ln 2) - lnx = ln(5/3)\]
Err wait, that should be ln(5/8) on the right side.
My teacher told us to set each side to the natural... which gave me: (x+3)ln2=xln5
Then I needed to get everything canceled out by cross multiplying... so I divided both sides by xln2
That's not right though. Unless you had 5^x on the right side originally.
Was it \(5x\) or \(5^x\)
the second one... I just looked in my book. Im so sorry
Ok good.
So yeah that's right. take the ln of both sides (or any log really)
Then solve for x. Don't plug anything into your calculator until you have something where x = something that has no x
(x+3)ln2=xln5 is correct for starting out
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
Get all terms with an x on one side.
Or that. Cross multiplying works fine
I usually multiply out products, but you don't need to here
Just be sure that you do (x+3)/x = ln5/ln2
Not just the 3.
I did and I got: x+3/x= 2.322/1
then: x+3=2.322x
Don't plug things in.
Keep solving the equation until you have x by itself. x = something that has no x.
Then plug in
Im not sure what/where.I am attempting to get x by itself? I thought that is what I was doing?
I think cross multiplying is just making this harder.
I just got a different answer of -4.425
Lets back up.
Ok..Im just trying to follow the instructions. But Im willing to try anything at this point
\[(x+3)ln2=xln5\] \[x(ln2)+3(ln2)=x(ln5)\] \[x(ln2)- x(ln5)= - 3(ln2)\] \[x[(ln2)- (ln5)]= - 3(ln2)\] \[x= \frac{- 3(ln2)}{(ln2)- (ln5)}\]
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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