MHB How can you solve $5^{x^2+8}=125^{2x}$ for x?

  • Thread starter Thread starter karush
  • Start date Start date
karush
Gold Member
MHB
Messages
3,240
Reaction score
5
$\tiny [6.3.74 Miliani HS$
Find x
$5^{x^2+8}=125^{2x}$
$\begin{array}{rlll}
\textsf{common base}&125^{2x}=(5^3)^{2x}=5^{6x}\\
\textsf{then } &x^2+8=6x\implies x^2-6x+8=0 \\
\textsf{factor}&(x-2)(x-4)=0\\
\textsf{get zeros}&x=2, \quad x=4\\
\end{array}$

should be ok
suggestions...
 
Mathematics news on Phys.org
that’s fine
 
I would suggest that you CHECK your answers!

If x= 2 then $x^2+ 8= 4+ 8= 12$ so $5^{x^2+ 8}= 5^{12}= 244140625$ while $125^{2x}= 125^{4}= 244140625$. Yes, they are equal!

If x= 4
then $x^2+ 8= 16+ 8= 24$ so $5^{x^2+ 8}= 5^{24}= 59604644775390625$ while $125^{2x}= 125^{8}= 59604644775390625$. Yes, they are equal!
 
If you live in Hawaii, how can you bear to do mathematics rather than being out on the beach every day?
 
there aways seems to be some non textbook trick with logs
 
Beer soaked ramblings follow.
Country Boy said:
If you live in Hawaii, how can you bear to do mathematics rather than being out on the beach every day?
Not everyone is fond of the sun and the beach.
Some would rather be indoors away from pesky flies and mosquitoes.
 
jonah said:
Beer soaked ramblings follow.

Not everyone is fond of the sun and the beach.
Some would rather be indoors away from pesky flies and mosquitoes.
im 76 and over weight I am embarrased to be seen in swimsuit
besides the mask restrictions have been ridiculus here. but they are getting ignored more and more finally,,
now they wondering if we will have condo colapse like florida :confused:
 
Country Boy said:
I would suggest that you CHECK your answers!

If x= 2 then $x^2+ 8= 4+ 8= 12$ so $5^{x^2+ 8}= 5^{12}= 244140625$ while $125^{2x}= 125^{4}= 244140625$. Yes, they are equal!

If x= 4
then $x^2+ 8= 16+ 8= 24$ so $5^{x^2+ 8}= 5^{24}= 59604644775390625$ while $125^{2x}= 125^{8}= 59604644775390625$. Yes, they are equal!
actually I am more interested in the steps
probably don't need the decimal unless there is some purpose for it
I ussually check with W|A if the book does not give answers
 
karush said:
actually I am more interested in the steps
probably don't need the decimal unless there is some purpose for it
I ussually check with W|A if the book does not give answers
Never trust the calculator!

-Dan
 

Similar threads

Replies
5
Views
1K
Replies
3
Views
1K
Replies
2
Views
1K
Replies
2
Views
1K
Replies
1
Views
1K
Replies
13
Views
2K
Replies
7
Views
2K
Replies
2
Views
1K
Replies
7
Views
2K
Replies
13
Views
2K
Back
Top