If log10 x - log10 x = 2 logx 10, then a possible value of x is given by:
Explanation:
log10 x - log10 x = 2 logx 10 ....(i)
Consider L.H.S of (i):
log10 x - 12 log10 x = 12 log10 x
Equating the L.H.S. and the R.H.S., we get,
log10 x = 4 logx 10
∴ log10 x = 4 logx 104
Now, let log10 x = logx 104 = y
∴ 10y = x and xy = 104
Solving these two equations, we get,
y = ±2
∴ x = 102 or x = 10–2
As x = 100 is not in the options,
∴ x = 10−2 = 1/100
Hence, option (b).
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