Solve for x :- 1) x^(-3) + x^(-3/2) = 2 2) 6(4^x + 9^x) = 6^x(4+9)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

1. x^-3 +x^-3/2 = 2

assume x^-3=y

\==> y+y^1/2 =2

==> y + y^1/2 -2=0

==> (y^1/2 +2)(y^1/2 -1)=0

==> y^1/2= -2 which is impossible

==> OR  y^1/2= 1 ==> y=1 ==> x= 1

2.   6(4^x + 9^x)= 6^x(9+6)

==> 6(4^x +9^x) = 6^x (13)

Divide by 6(6^x)

==> (4^x + 9^x)/6^x= 13/6

==> 4^x/6^x  + 9^x/6^x = 13/6

==> (2/3)^x + (3/2)^x = 13/6

Now assume that (2/3)^x =y

==> y+ 1/y = 13/9

==> y^2 + 1 = (13/9)y

==> y^2-(13/9)y +1 =0

==> [y-(3/2)][y-(2/3)]=0

==> y = 3/2 ==> x= -1

 OR y= 2/3 ==> x=1

 

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial