Tried this equation everywhere

[Barabbas]

This costed me 2 pts on a quiz
(2x+7)^(2x+7)=3125
Probably getting the answer to this tomorrow but if someone could solve it would be cool.
Thank you.

[Guest]

Are there possible answers?

[Guest]

If x=-1 ,then

[tex](2(-1)+7)^{(2(-1)+7)}[/tex]=

=[tex]5^{5}[/tex]=(5.5)(5.5)5=

=25.25.5=625.5=

=3 125

So -1 is root.

[Guest]

This costed me 2 pts on a quiz
(2x+7)^(2x+7)=3125
Probably getting the answer to this tomorrow but if someone could solve it would be cool.
Thank you.

The first thing I would do is let y= 2x+ 7 so the equation becomes y^y= 3125. Then I would think about factoring 3125. Obviously 25 is a factor: 3125= 25(125). And 125= 5(25) so 3125= (25)(25)(5)= 5^5. Aha! y^y= 5^5 so y= 2x+ 7= 5. 2x= 5- 7= -2 and x= -1.

[Guest]

Seeing that "3125" the first thing I would do is factor it. [tex]3125= 5^5[/tex]. So I want 2x+ 7= 5.