If log 2 x-log x 2-10-3-log 2 y-log y 2 and x-y- thenx -y3 is equal to

The correct option is A Given, log_2 x+ 1/log_2 x = 3+1/3 = log_2 y + 1/log_2 x ⇒ log_2 x=3, log_2 y = 1/2 [∵ x ≠ y] ⇒ x = 2^3 and y = 2^1/3 Hence, ...

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Byju's Answer

Standard XII

Mathematics

Global Maxima

If log 2 x+lo...

Question

If $l o g_{2} x + l o g_{x} 2 = \frac{10}{3} = l o g_{2} y + l o g_{y} 2 a n d x \neq y, t h e n x + y^{3}$ is equal to

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Solution

The correct option is A
$G i v e n, l o g_{2} x + \frac{1}{l o g_{2} x} = 3 + \frac{1}{3} = l o g_{2} y + \frac{1}{l o g_{2} x} \Rightarrow l o g_{2} x = 3, l o g_{2} y = \frac{1}{2} [∵ x \neq y] \Rightarrow x = 2^{3} a n d y = 2^{1 / 3} H e n c e, x + y^{3} = 8 + 2 = 10$

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Q. If

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If log2x+logx2=103=log2y+logy2 and x≠y,thenx+y3 is equal to

The correct option is A Given,log2 x+1log2x=3+13=log2 y+1log2x⇒log2 x=3, log2 y=12 [∵x≠y]⇒x=23 and y=21/3Hence,x+y3=8+2=10

If $l o g_{2} x + l o g_{x} 2 = \frac{10}{3} = l o g_{2} y + l o g_{y} 2 a n d x \neq y, t h e n x + y^{3}$ is equal to

The correct option is A
$G i v e n, l o g_{2} x + \frac{1}{l o g_{2} x} = 3 + \frac{1}{3} = l o g_{2} y + \frac{1}{l o g_{2} x} \Rightarrow l o g_{2} x = 3, l o g_{2} y = \frac{1}{2} [∵ x \neq y] \Rightarrow x = 2^{3} a n d y = 2^{1 / 3} H e n c e, x + y^{3} = 8 + 2 = 10$