1. Find value of `x` where Geometric mean`=8` for data `4,x`

Solution:
GM `=sqrt((4 xx x))`

`8=sqrt((4 xx x))`

`8^2=4 xx x`

`x=64/4`

`x=16`

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2. Find value of `x` where Geometric mean`=4` for data `2,x,8`

Solution:
GM `=root (3)((2 xx x xx 8))`

`4=root (3)((2 xx x xx 8))`

`4^3=16 xx x`

`x=64/16`

`x=4`

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3. Find value of `x` where Geometric mean`=8` for data `x,8,16`

Solution:
GM `=root (3)((x xx 8 xx 16))`

`8=root (3)((x xx 8 xx 16))`

`8^3=128 xx x`

`x=512/128`

`x=4`

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4. Find value of `x` where Geometric mean`=4` for data `1,x,8,16`

Solution:
GM `=root (4)((1 xx x xx 8 xx 16))`

`4=root (4)((1 xx x xx 8 xx 16))`

`4^4=128 xx x`

`x=256/128`

`x=2`

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5. Find value of `x` where Geometric mean`=9` for data `1,3,9,x,81`

Solution:
GM `=root (5)((1 xx 3 xx 9 xx x xx 81))`

`9=root (5)((1 xx 3 xx 9 xx x xx 81))`

`9^5=2187 xx x`

`x=59049/2187`

`x=27`

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6. Find value of `x` where Geometric mean`=8` for data `1,x,16,64`

Solution:
GM `=root (4)((1 xx x xx 16 xx 64))`

`8=root (4)((1 xx x xx 16 xx 64))`

`8^4=1024 xx x`

`x=4096/1024`

`x=4`

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