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Logarithmic Inequalities

If log2x+log2...

Question

If ${log}_{2} x + {log}_{2} y \geq 6$ , then the least value of $x y$ is

A

64

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B

32

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C

16

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D

8

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Solution

The correct option is A $64$
${log}_{2} x + {log}_{2} y \geq 6 \Rightarrow {log}_{2} (x y) \geq 6 \Rightarrow x y \geq 2^{6} = 64$

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Similar questions

{log}_{2} x + {log}_{2} y \geq 6,

then the least value of x+y is

{log}_{2} x + {log}_{2} y \geq 6

, then the least value of

x y

{log}_{2} (x + y) = 3

{log}_{2} x + {log}_{2} y = 2 + {log}_{2} 3

, then the values of

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y

Q. Solve the following systems of equations.

2 l o g_{4} (y + 1) + l o g_{2} y = l o g_{2} (\frac{x}{y} - 2), 5 + l o g_{2} \frac{y}{x} = \frac{6}{l o g_{2} \frac{x}{y}} .

{log}_{2} x + {log}_{x} 2 = \frac{10}{3} = {log}_{2} y + {log}_{y} 2

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