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Question

If log10a+log10b=log10(a+b), then

A
a=b=2
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B
a=b=1
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C
a=b21b
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D
a=bb1
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Solution

The correct options are
A a=b=2
D a=bb1
Given,
log10a+log10b=log10(a+b)
log10ab=log10(a+b) [loga+logb=logab]
ab=a+b.
Dividing throughout by b we get
a=ab+1aab=1a(11b)=1a(b1b)=1a=bb1
Also, a=b=2 satisfies the given equation.
Hence, options A and D are correct.

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