# 1/log(base2⁡)100 -1/log(base4⁡)100 +1/log(base5⁡)100 | Quantitative Aptitude - Algebra - Logarithms

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Geometry– Triangles – A triangle ABC has area 32 sq units …. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

## CAT 2018 – Slot 2 - Logarithms - Question 4 - 1/log(base2⁡)100 -1/log(base4⁡)100 +1/log(base5⁡)100

Q. 4:1/log(base2⁡)100 -1/log(base4)⁡100 +1/log(base5)⁡100 -1/log(base10)⁡100 +1/log(base20⁡)100 -1/log(base25)⁡100 +1/log(base50)⁡100 —?
1. 1/2
2. 0
3. 10
4. −4

Using log(basea)⁡b = 1/log(baseb⁡)a

1/log(base2⁡)100 -1/log(base4⁡)100 +1/log(base5⁡)100 -1/log(base10)⁡100 +1/log(base20)⁡100 -1/log(base25)⁡100 +1/log(base50)⁡100

= log(base100)⁡2- log(base100)⁡4+ log(base100⁡)5-log(base100⁡)10+ log(base100⁡)20-log(base100⁡)25+log(base100⁡)50

=log(base100)⁡ (2×5×20×50)/(4×10×25)

=log(base(10^2 ))⁡10=1/2

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