Rapid Revision · Quantitative Aptitude
Logs turn multiplication into addition and powers into products. A handful of rules cracks most log questions in seconds, no calculator needed.
If you read nothing else tonight, read these 6 lines.
Every formula for logarithms in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Definition
log_b(x) = y <=> b^y = x
Product & quotient
log(mn) = log m + log n log(m/n) = log m - log n
Power rule
log(m^p) = p x log m
Change of base
log_b(x) = log_a(x) / log_a(b)
Identities
log_b(b) = 1 log_b(1) = 0 b^(log_b x) = x
Digit count
digits of N = floor(log10 N) + 1
6 cards, each one idea: what it is, a worked example, and the trap to dodge.
log_b(x) = y is the same statement as b^y = x. Most 'find the value' questions are solved just by rewriting the log form as an index form.
log_2(32) = 5 because 2^5 = 32.
Trap: Base must be positive and not 1; the argument must be strictly positive. log of 0 or a negative number is undefined.
Product, quotient and power rules are all you need to expand or compress a log expression. A term that looks scary usually collapses with these.
log(8/3) = log 8 - log 3 = 3 log 2 - log 3.
The number of digits before the decimal in N is floor(log10 N) + 1. This is how 'how many digits in 2^100' questions are meant to be solved.
digits in 2^100 = floor(100 x 0.301) + 1 = floor(30.1) + 1 = 31.
Get both sides to the same base, then the arguments (or the exponents) must be equal. If the bases differ, use change of base first.
log_2(x) + log_2(x - 2) = 3 -> log_2(x(x-2)) = 3 -> x(x-2) = 8 -> x = 4.
Trap: Reject any root that makes an argument zero or negative; here x = -2 is discarded.
Most base-10 questions expect you to derive logs from log 2 = 0.301 and log 3 = 0.477 using the three rules.
log 6 = log 2 + log 3 = 0.778; log 5 = log(10/2) = 1 - 0.301 = 0.699.
In aptitude, log with no base means base 10; ln means base e. They differ only by a constant factor, so the rules are identical for both.
Trap: log(a + b) is NOT log a + log b. The sum rule is for products, never for sums.
A recap is not practice. These are the creators we rate for real depth on logarithms; full credit to each.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.