If ${a^x} = {b^y} = {c^z} = {d^w},$ then ${\log _a}\left( {bcd} \right)$ equals to

$\frac{1}{x}\left( {\frac{1}{y} + \frac{1}{z} + \frac{1}{w}} \right)$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

{a^x} = {b^y} = {c^z} = {d^w},

then

{\log _a}\left( {bcd} \right)

equals to

View answer and explanation

Correct option: B

x\left( {\frac{1}{y} + \frac{1}{z} + \frac{1}{w}} \right)

Option B (

x\left( {\frac{1}{y} + \frac{1}{z} + \frac{1}{w}} \right)

) is correct because by taking logarithms and manipulating the equations,

{\log _a}\left( {bcd} \right)

can be expressed as

x\left( {\frac{1}{y} + \frac{1}{z} + \frac{1}{w}} \right)

Practice All Chapter MCQs →

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(B \cup C)-A

a,b,c

a,x,b

b,y,c

{x^2},{b^2},{y^2}

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

y

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

y=x-2

\sum\limits_{{i=0}}^{2012} a_i

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

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A P

a, b

G P

a, b, c

\frac{3}{4}