Tayarri LCAT
LCAT Math, Advanced Math

Logarithms for the LCAT: lesson and practice

A logarithm answers the question "what power?". logb x = k means bk = x, so log2 8 = 3 because 23 = 8. Two rules cover most LCAT questions: log M + log N = log MN, and log(xn) = n log x.

Loading practice…

No calculator on the LCAT. LUMS’s official sample says calculators are not allowed, so every practice question here can be solved by hand.
RuleExample
logb x = k ⇔ bk = xlog3 81 = 4
log M + log N = log MNlog2 8 + log2 4 = 3 + 2 = 5
log(xn) = n log xif log3 x = 4, log3 x2 = 8
logb b = 1, logb 1 = 0log10 10 = 1

The LUMS sample question

Given logx 16 = 4 and logx 2 = y, find y.

x4 = 16, so x = 2
y = log2 2 = 1
Memorize powers of 2 up to 210 = 1024, of 3 up to 35 = 243, and of 5 up to 54 = 625. They make log questions quick without a calculator.

Common mistakes

Answering with the number, not the powerlog2 8 is 3, not 8.
Multiplying logslog2 8 + log2 4 = 5, not 6.
Squaring the logIf log x = 4, log x2 = 8, not 16.

Sample questions with answers

1. What is the value of log₃ 81?
  1. 3
  2. 4 (correct)
  3. 27
  4. 81

3⁴ = 81, so the answer is 4.

2. If log₂ x = 5, what is x?
  1. 10
  2. 25
  3. 32 (correct)
  4. 7

2⁵ = 32.

3. If logₓ 16 = 4 and logₓ 2 = y, what is y?
  1. 1 (correct)
  2. 2
  3. 3
  4. 4

x = 2, so y = log₂ 2 = 1.

Frequently asked questions

Are logarithms on the LCAT?

Yes. LUMS’s official LCAT guidelines list logarithms among the math topics, and its sample questions include a logarithm problem.

Do I need a calculator for logs?

No. LCAT log questions use numbers that are powers of small bases, such as 2, 3, 5 and 10.

How do I check a log answer by hand?

Turn it back into a power. If you found log₂ 32 = 5, check that 2⁵ = 32.

Keep going