If a^{x}=b^{y}=c²=d^{w}, then _{a}(b c d)=

Correct Answer is : x( 1y+ 1z+ 1w)x≤ft(\;1/y+\;1/z+\;1/w)x(y1+z1+w1)

Correct Answer is : x( 1y+ 1z+ 1w)x≤ft(\;1/y+\;1/z+\;1/w)x(y1+z1+w1)

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Logarithms

Question : 31 of 85

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a^{x}=b^{y}=c^{2}=d^{w},

\log_{a}(b c d)=

Solution:

Concept:

Express each base in terms of a common power using the given equality.

Explanation:

Let

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

(assuming

c^{z}

as per standard problem).

Then

a = k^{1/x}

b = k^{1/y}

c = k^{1/z}

d = k^{1/w}

bcd = k^{1/y + 1/z + 1/w}

Now

\log_a(bcd) = \log_{k^{1/x}}(k^{1/y + 1/z + 1/w}) = \frac{1/y + 1/z + 1/w}{1/x} = x\left(\frac{1}{y}+\frac{1}{z}+\frac{1}{w}\right)

Answer:

Option B:

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

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