If $x,\;y,\;z$ are in GP and ${a^x} = {b^y} = {c^z}$, then

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

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Analyzing +4 | -1

x,\;y,\;z

are in GP and

{a^x} = {b^y} = {c^z}

, then

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Correct option: B

{\log _b}a = {\log _c}b

Option B (

{\log _b}a = {\log _c}b

) is correct because given that x, y, z are in GP and

{a^x} = {b^y} = {c^z}

, by taking logarithms and using the properties of logarithms, we can derive the relationship

{\log _b}a = {\log _c}b

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\left|\sum\limits_{r=1}^n z_r\right|

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\alpha, \beta

\gamma

|\alpha-\beta|

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z \in C

2x = - 1 + \sqrt 3 i

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}