Mathematics · 24 questions in the exam

Logarithms and exponentials

Q: Exponential equations

Write both sides with the same base and equate exponents. If a power appears with its square, set t = aˣ > 0 and solve a quadratic. Otherwise take logarithms of both sides. 4ˣ − 3·2ˣ − 4 = 0: t = 2ˣ ⇒ t = 4 ⇒ x = 2

What a logarithm means, its identities, the graphs of aˣ and logₐx, and exponential and logarithmic equations and inequalities. Logarithms and exponentials is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 6 lessons, each with the rule that solves it and a diagram.

Exponential and logarithmic form

log_b a is the exponent you put on b to get a: log_b a = c ⇔ bᶜ = a. It needs b > 0, b ≠ 1 and a > 0. ln uses base e and log base 10.

Rulelog₂ 32 = 5 because 2⁵ = 32

Logarithm identities

A logarithm turns products into sums, quotients into differences and powers into multipliers. Change the base with log_b a = log a / log b. There is no rule for log(a + b).

Rulelog(ab) = log a + log b; log(aⁿ) = n·log a

Exponential and logarithmic graphs

bˣ passes through (0, 1), is always positive and has the x-axis as an asymptote; log_b x passes through (1, 0), exists only for x > 0 and has the y-axis as an asymptote. Both rise if b > 1 and fall if 0 < b < 1.

Ruley = bˣ and y = log_b x mirror each other in y = x

Exponential equations

Write both sides with the same base and equate exponents. If a power appears with its square, set t = aˣ > 0 and solve a quadratic. Otherwise take logarithms of both sides.

Rule4ˣ − 3·2ˣ − 4 = 0: t = 2ˣ ⇒ t = 4 ⇒ x = 2

Logarithmic equations

First write the conditions (every argument > 0), then combine the logs into one and remove it: log_b A = log_b B ⇒ A = B. Keep only the solutions that meet the conditions.

Rulelog x + log(x − 3) = 1 ⇒ x(x − 3) = 10 ⇒ x = 5

Exponential and logarithmic inequalities

With a base above 1, compare exponents (or arguments) in the same direction; with a base between 0 and 1, reverse it. For logarithms, intersect the result with the domain.

Rule(1/2)ˣ > 1/8 ⇔ x < 3

What is the Bocconi Test format?

Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.

Questions / time: 50 / 75 minutes
Distribution: 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
Scoring: +1 correct · 0 blank · −0.2 wrong
Question languages: English · Italian
Three-option questions: Some critical thinking questions have three options; a wrong answer there costs −0.33
Minimum score: Below 17 points the test is not considered for selection
AI degree: Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
Law test: A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring

Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)

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