Help!!
$2^{3x 1}=5^{5-x}$

Question

Enorym · Answer

@umm @Elsa213 @ThisGirlPretty

ThisGirlPretty · Answer

@563blackghost @Shadow

sillybilly123 · Answer

sure you got that right?!?!  screengrab?

Enorym · Answer

$ 2^{3x+1}=5^{5-x}$
I forgot the addition, sorry @sillybilly123

sillybilly123 · Answer

so take logs, natural logs if you like

$2^{3x+1}=5^{5-x}$

$\ln ( 2^{3x+1} )= \ln ( 5^{5-x})$

$(3x+1) \ln 2 = (5-x) \ln 5$

And so on, solving for x

Enorym · Answer

I got there, then I did
$$(3x)ln2+ln2=(5)ln5+(-x)ln5$$

sillybilly123 · Answer

sure....and park the x's on the LHS and the non-x's on RHS

Enorym · Answer

$$3x ~ln~2+x ln~5= 5ln~5-ln~2$$

sillybilly123 · Answer

$3x \ln~2+x \ln~5= 5 \ln~5-\ln~2$

put a slash in front of the *ln* in tour Latex, smartens it up, like this

$x (3\ln~2+ \ln~5)= 5 \ln~5-\ln~2$

$\implies x = \dfrac{5 \ln 5-\ln 2}{3\ln 2+ \ln 5}  $

sillybilly123 · Answer

the slash also creates a space afterwards so you don't need to use copious ~'s

Enorym · Answer

Ah, thanks

sillybilly123 · Answer

mp/np

Enorym · Answer

Too many abbreviations

sillybilly123 · Answer

you can do more stuff with it like, eg just taking the numerator:

$5 \ln 5-\ln 2 = \ln \dfrac{5^5}{2}$

but the next simplification is the calculator....turning x into a simple number

Enorym · Answer

Ah, I am not allowed to use a calculator for this part

sillybilly123 · Answer

well i think that means you're done.

Enorym · Answer

Thanks a lot, sillybilly

sillybilly123 · Answer

TU

Enorym · Answer

A lot of abbreviations, I think I may need to update myself in those.