Surds and Indices Practice Test 2

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Question : 16 of 17

Marks: +1, -0

Given that

2^x = 4^y = 8^z

and

(1/{2x}+1/{4y}+1/{6z})=24/7

, then find the value of z.

$7 /64$
$7 /48$
$7 /32$
$7 /16$

Solution:

2^x = 4^y = 8^z

2^x = 2^{2y} = 2^{3z}

Hence,

x = 2y = 3z

Now,

1/{2x}+1/{4y}+1/{6z} =24/7

⇒1/{6z}+1/{6z}+1/{6z} =24/7

⇒3/{6z}=24/7

⇒z=7/48

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