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Question

If (21.4)a=(0.00214)b=100, then the value of (1a−1b), is

A
0
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B
1
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C
2
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D
4
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Solution

The correct option is C 2
Given that
(21.4)a=(0.00214)b=100
(21.4)a=100,(0.00214)b=100
Applying log on both the sides, we get
a=log21.4100,b=log0.00214100
1a1b=1log21.41001log0.00214100, [logab=1logba]
1a1b=log10021.4log1000.00214
1a1b=log10021.40.00214=log1001002=2log100100=2,
[logalogb=logab]

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