If 2 x </msup> = 3 y </msup> = 6 &#x2

Hailie Blevins 2022-06-27 Answered
If 2 x = 3 y = 6 z and x , y , z 0 then prove that:
1 x + 1 y + 1 z = 0
I have tried starting with taking logartithms, but that gives just some more equations.
Any specific way to solve these type of problems?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

rioolpijpgp
Answered 2022-06-28 Author has 19 answers
2 x = 3 y = 6 z = k say, then 2 = k 1 x , 3 = k 1 y , 6 = k 1 z now can you go on?
then k 1 z = 6 = 2 × 3 = k 1 x × k 1 y = k 1 x + 1 y

We have step-by-step solutions for your answer!

arridsd9
Answered 2022-06-29 Author has 12 answers
2 x = 3 y = 6 z = k
so
x = log 2 k
y = log 3 k
z = log 6 k
so
1 x + 1 y + 1 z = log k 2 + l o g k 3 log k 6
= log k 2 × 3 6
= 0

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-06-22
How many solutions are there to this equation?
x 2 y 2 = z y 2 z 2 = x z 2 x 2 = y
asked 2022-09-20
Find homogeneous system of linear equations whose solution space is: V = span((1,-2,4,3),(1,-1,6,4),(3,-8,8,3)).
First I found vectors were linearly dependent, so I discarded the third vector to form a new base. Next I figured system will have 2 free variables and if we would use gauss-jordan elimination on matrix of a system we would get this:
[ 1 0 0 1 ]
asked 2022-04-27

Solve the system by substitution.
x-4y=-8
5y-1=x

asked 2022-05-19
For how many values of α does this system of equations have infinitely many solutions ?
( 2 1 4 4 3 12 1 2 8 ) ( x y z ) = ( α 5 7 )
asked 2021-01-30
Solve the following simultaneous equations. 3a+5b=26, a+5b=22
asked 2022-06-12
Prove that a = 2 , b = 2 , c = 2 for a system of three equations.
Let us consider a system equations :
(i) a 3 + b = 3 a + 4 (ii) 2 b 3 + c = 6 b + 6 (iii) 3 c 3 + a = 9 c + 8
I have tried with the following steps :
6 × ( i ) + 3 × ( i i ) + 2 × (iii) gives:
6 ( a 3 + b 3 + c 3 ) + 6 b + 3 c + 2 a = 18 ( a + b + c ) + 58.
But I don't know how to solve in this way. By inspection method I have seen a = b = c = 2.
asked 2022-05-21
Test the consistency of the system of linear equations
4 x 5 y + z = 2 3 x + y 2 z = 9 x + 4 y + z = 5