Question

2^x=4^y=8^z ; xyz=288 ; find value of 1/2x + 1/4y + 1/8z

Answer 1

Answer:

Step-by-step explanation:

2ˣ=4ʸ=8ᶻ

Making the bases same

=>2ˣ=2²ʸ=2³ᶻ

Since bases are same, therefore equating the exponents

=>x=2y=3z

=>x=3z (i) , y=3z/2(ii)

xyz=288

replacing x and y with equations (i)and(ii)

=> 3z*(3z/2)*z=288

=>9z³=288*2

=>9z³= 576

=>z³=576/9

=>z³=64

=>z=4

therefore x=12, y=6

its difficult to understand where exactly the variables are to be placed in the second part of the question(i.e. whether the variables are in the numerator or denominator), so I will be doing it both ways-

1) 1/2*x+ 1/4*y+1/8*z

=1/2*12+ 1/4*6+1/8*4

=1/24+1/24+1/32

=1/12+1/32

=8/96+3/96

=11/96

2) 1*x/2+1*y/4+1*z/8

=1*12/2+1*6/4+1*4/8

=6+3/2+1/2

=12/2+3/2+1/2

=16/2

=8

hope it helps. if yes, please mark it the brainliest