carlos was asked to solve the exponential equation for x. why is his answer wrong?What should he have done differently?

Question

anonymous · Answer

3^x+2=9^4
3^2(x+2)=9^4
9^x+2=9^4
x+2=4
-2      -2
x=2

anonymous · Answer

@Agl202

anonymous · Answer

@kashmirkid

anonymous · Answer

Were they not supposed to square it?

anonymous · Answer

@kitkat16 @__yasmeen__

agl202 · Answer

http://openstudy.com/study#/updates/53bc41e1e4b0f3a650f866bb

anonymous · Answer

@johnweldon1993 @Owlcoffee @IamaBoss @KendrickLamar2014 @triciaal

anonymous · Answer

im sorry this isnt something im great at but why did Carlos do this step 3^2(x+2)=9^4

anonymous · Answer

@Agl202 They never answered it though :/

anonymous · Answer

@kashmirkid thank you! and that's what I was wondering, I think that's the part he messed up on when he sqyared it right?

anonymous · Answer

can you take a screenshot of the question because this is confusing

anonymous · Answer

Yea I will!

anonymous · Answer

attachment

anonymous · Answer

@__yasmeen__

kitkat16 · Answer

that screen shot doesnt show anything

anonymous · Answer

yeah^^^

owlcoffee · Answer

The answer Carlos gave, is wron ing the followng two steps:
$$3^{x +2}=9^4$$
$$3^{2(x +2)}=9^4$$
it's quite evident, but what he did is what I like to call "disbalance of equation" because we can see that Carlo squared the left side of the equation but did not square the right side.
this will alter the result of the calculations, the correct way is:
$$(3^{x+2})^2 = (9^4)^2$$
$$9^{(x+2)}=9^8$$
$$x+2=8$$
$$x=6$$
and we can verify it:
$$3^{(6+2)}=9^4$$
$$3^8 = 9^4$$
$$6561=6561$$