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Napier and the logarithm: the marvellous abbreviation

Today, for many students, the logarithm is a bogeyman: a strange word, a $\log$ that appears out of nowhere and rules to memorise. In the seventeenth century it was the opposite. It was Europe’s calculator, the tool that saved astronomers, navigators and accountants months of work. The old texts on this site said the logarithm was the purest example of mirabilis abbreviatio, the marvellous abbreviation. And its inventor agreed: the title of his book begins with the word marvellous.

October 10, 2026 Read
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ENEM 2025 – Solved mathematics: questions 166 to 180

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2025 was administered on the 2nd day and will from question 136 to 180. This post addresses questions 166 to 180. The numbering used here is that of the Notebook 5 – Yellow; us In other notebooks the same questions appear in a different order. Template Question Subject Template 166 Volume Units D 167 Agricultural production and line graph A 168 Volume: cylinder minus prism B 169 Probability with data E 170 Units of measurement A 171 Sequences: expression of the general term D 172 Chart reading and fuel cost D 173 Cost Comparison E 174 Volume of the parallelepiped B 175 Spatial geometry: cylinder in prism E 176 Logarithm and quadratic function A 177 Area of ​​the semicircle A 178 Equation: installments of financing Canceled 179 Combinatorial analysis: combinations C 180 Average speed C Question 166: Ice cream cups (volume units) Statement The owner of an ice cream shop stores ice cream in 20 000 cm³ containers. He serves the ice cream in cups, in portions of 250 mL.

September 27, 2026 Read
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ENEM 2024 – Solved mathematics: questions 136 to 150

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2024 was administered on the 2nd day and will from question 136 to 180. This post addresses questions 136 to 150. The numbering used here is that of the Notebook 5 – Yellow; us In other notebooks the same questions appear in a different order. Template Question Subject Template 136 Related function: production cost C 137 Statistics: median E 138 Proportional division C 139 Combinatorial analysis: combinations E 140 Probability of independent events B 141 Reason: demographic density E 142 Fractions and mixed numbers D 143 Increasing plots (logical reasoning) A 144 Arc length: pulleys and belt D 145 equilateral triangle: circumcenter C 146 Graph Reading: Sine Amplitude A 147 Areas of regular polygons A 148 Speed ​​and furniture finding D 149 Probability without replacement E 150 Logarithm: Richter scale C Question 136: Cost of producing backpacks (related function) Statement A company produces custom school backpacks. This company has a cost total production, composed of a fixed cost, which does not depend on the number of backpacks, plus a variable cost, which is proportional to the number of backpacks produced. The total cost grows linearly, and the table shows this cost for three quantities of backpacks produced.

September 26, 2026 Read
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ENEM 2023 – Solved mathematics: questions 151 to 165

Source: INEP – proof and template of the 2nd day, Notebook 5 – Yellow. The ENEM Mathematics and Technologies test 2023 was administered on the 2nd day and will from question 136 to 180. This post addresses questions 151 to 165. The numbering used here is that of the Notebook 5 – Yellow; us In other notebooks the same questions appear in a different order. Template Question Subject Template 151 Percentage: daycare waiting list B 152 Sequences: pentagonal numbers E 153 Periodic functions: Ferris wheel A 154 Scatter and percentage plot B 155 Profit, revenue and cost D 156 Exponential growth D 157 Multiplicative principle and probability A 158 Conditional probability in steps A 159 Geometric progression D 160 Quadratic function: minimum value D 161 Percentage and algebraic expression A 162 Graph reading (parametric curve) B 163 Logarithms: sound level in decibels B 164 Volume of cone, frustum and cylinder B 165 Weighted average C Question 151: New rooms for the daycare center (percentage) Statement In January last year, the management of a factory opened a daycare center for children of its employees, with 10 rooms, each with the capacity to serve 10 children each year. Vacancies are drawn among employees’ children. registered, while those not included in the draw form a waiting list. Last year, the waiting list had 400 names, and this year, that number grew 10%.

September 26, 2026 Read
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