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If a^(x) = b^(y) = c^(z) = d^(w)," show...

If ` a^(x) = b^(y) = c^(z) = d^(w)," show that " log_(a) (bcd) = x (1/y+1/z+1/w)`.

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`log_(a)(bcd)=log_(a) b+log_(a) c+ log_(a) d`
Now` a^(x) = b^(y)`
` or (log b)/(log a) = x/y`
` or log_(a)b = x/y`
Similarly, ` log_(a) c= x/z and log_(a) d = x/w`
` rArr log_(a) (bcd) = log_(a) b+ log_(a) c+ log_(a) d`
`= x(1/y+1/z+1/w)`
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