× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
5
o
5
4
m
4
b
4
x
4
a
4
l
4
t
4
S
4
m
3
s
3
New Topic  
Mathguy3000 Mathguy3000
wrote...
Posts: 15
Rep: 3 0
5 years ago
2(27)^x = 9^x+1
Read 157 times
1 Reply

Related Topics

Replies
wrote...
Valued Member
Educator
5 years ago
\(2(27)^x=9^x+1\)

\(2(3\cdot 9)^x=9^x+1\)

\(2(3^x\cdot 9^x)=9^x+1\)

\(2(3^x\cdot \left(3\cdot 3\right)^x)=9^x+1\)

\(2(3^x\cdot 3^x\cdot 3^x)=3^x\cdot3^x+1\)

Set \(u=3^x\):

\(2(u^3)=u^2+1\)

\(2u^3-u^2-1=0\)

Something's wrong...

Let's try again...

\(2(27)^x=9^x+1\)

\(2(3^3)^x=9^x+1\)

\(2(3^x)^3=\left(3\cdot 3\right)^x+1\)

\(2(3^x)^3=3^x\cdot 3^x+1\)

Set \(u=3^x\):

\(2(u)^3=u^2+1\)

Yikes, we've got a cubic function! You could graph it...

That's your answer, \(x = 1\).
 Attached file 
Thumbnail(s):
You must login or register to gain access to this attachment.
New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers
  1101 People Browsing
Related Images
  
 91
  
 213
  
 225
Your Opinion