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42 results for “logarithm”
Mathematics Logarithmic notation and its link to index form Laws of logarithms: product, quotient, power and roots, derived from the laws of indices Simplification of logarithmic expressions; logarithmic equations with u…
…nd why that turns out to be useful. The laws of indices from the previous lesson. Mathematics 1.2 Indices and Logarithms You know that 2 3 = 8. Now turn the question round: To what power must 2 be raised to give 8? The a…
A common logarithm is the power of 10; log with no base written means base 10. That a logarithm is an index rewritten, from Introducing logarithms, and powers of 10. Mathematics 1.2 Indices and Logarithms The last logari…
A common logarithm is the index when a number is written as a power of 10. Read it from the power, from tables, or from a calculator. Index form, powers of 10, and 10 0 = 1. Mathematics 1.3 Indices and Logarithms 102 = 1…
The pH scale is logarithmic: a drop of one unit means ten times more H+. Reading the pH scale. Chemistry 2.1 Acids and bases Learners often treat pH 3 as 'a bit more acidic than pH 5'. That error follows them into soil s…
…als a as log base b of a equals c, and reject bases or arguments that make the log undefined. Grade 10 common logarithms as powers of 10, and zero, negative and fractional indices. Mathematics 1.4 Logarithms II A logarit…
…ot that makes an argument zero or negative. Log laws, and solving a quadratic by factorising. Mathematics 1.4 Logarithms II An equation with a logarithm is first turned back into an index, or into one log equal to a numb…
…omain of a log, and the given values log base 10 of 2 = 0.3010 and log base 10 of 3 = 0.4771. Mathematics 1.4 Logarithms II Logarithms answer how many times a multiplication has been repeated. They also turn a base-2 que…
…ematics state and apply the laws of indices work with zero, negative and fractional indices relate indices to logarithms use logarithms to solve simple equations Use a scientific calculator to check answers obtained by a…
1. Write log 3 + log 7 as a single logarithm. 2. Write log 72 - log 8 as a single logarithm and evaluate it. 3. Write 4 log 2 as a single logarithm and evaluate it. 4. log 5 + log 2. Why is the answer 1? 5. Why is log 6 …
…Not all bases are alkalis - copper oxide is a base but does not dissolve. Properties compared The pH scale is logarithmic, and this is regularly misunderstood. Each unit is a tenfold change. pH 3 is not slightly more aci…
…ind logs of products, quotients and powers. The product, quotient and power laws for base 10. Mathematics 1.4 Logarithms II Four-decimal common logs are enough for a careful numerical calculation. Take these as given, al…
…. The power gain is the product of the voltage gain and the current gain. Gains are also often expressed on a logarithmic scale in decibels. Our question: How does a BJT amplifier work? Gains Current gain (A i). A i = Io…
…ted: turning a hard operation into an easy one. Multiplication becomes addition. Napier had already published logarithms in 1614 for the same purpose, and the whole history of computing is the repetition of this trick - …
…f the log. The product law, and fractional indices such as a square root being the power 1/2. Mathematics 1.4 Logarithms II A power inside a log can move to the front as a multiplier. A root is the same law with a unit f…
…ation. Log notation, and the index laws for multiplying and dividing powers of the same base. Mathematics 1.4 Logarithms II The log laws are the index laws written the other way round. They are derived, not memorised fir…
…owers of the same base into a single log, then evaluate it. Product, quotient and power laws. Mathematics 1.4 Logarithms II A long log expression usually collapses. Combine the arguments first, or evaluate each easy log …
Logs turn a product into a sum, a quotient into a difference, and a power into a multiplication. Common logarithms: log n is the power of 10 that gives n. Mathematics 1.2 Indices and Logarithms Indices: multiplying numbe…
…. The same earthquake has many intensities - high near the epicentre, low far away. The Richter scale is also logarithmic. Each whole number is about ten times the ground movement and roughly thirty times the energy. A m…
1. Write 4 to the power 3 equals 64 in logarithm form, and evaluate it. 2. Evaluate log base 10 of 0.001. 3. Which of these is defined: log base 2 of 8, log base 2 of 0, log base -2 of 4? Give the value of the defined on…
…and a straight gradient. Mathematics 2.6 Graphical Methods A power hiding in the input can be brought down by logarithms. If y = ax n, then log y = log a + n log x. Plot log y against log x. The gradient is the power n, …
…the indices. Zero, negative and fractional indices from the previous two lessons. Mathematics 1.2 Indices and Logarithms The laws only combine powers of the same base. 23 x 32 is not 65 and not 25. It is just 8 x 9 = 72.…
…divide, raise to a power and take a root by adding, subtracting or scaling logs, then taking the antilog. The logarithm laws, and how to read a characteristic and a mantissa. Mathematics 1.2 Indices and Logarithms Before…
…. Cancel equal factors. Multiplication law a m x a n = a (m+n) for the same base. Mathematics 1.3 Indices and Logarithms Barasa divides 25 by 22. Five 2s on top, two 2s underneath. Cancel two pairs. Three 2s remain: 23 =…
…t. Zero and negative indices from the previous lesson, and square and cube roots. Mathematics 1.2 Indices and Logarithms 161/2 looks new. It is not. The index laws force it to be a square root. Because (161/2) x (161/2) …
…ors of the base. Grade 8 squares (two factors) and Grade 9 cubes (three factors). Mathematics 1.3 Indices and Logarithms Grade 8 wrote 5 x 5 as 5 squared. Grade 9 wrote 5 x 5 x 5 as 5 cubed. Index form writes any number …
…locate the event. Three ways of measuring an earthquake ### Using the scales, not just naming them Richter is logarithmic - each whole number is about thirty times the energy, as the first lesson showed. It was designed …
…e law by expanding factors. Index form, base and index, from the previous lesson. Mathematics 1.3 Indices and Logarithms Njeri multiplies 23 by 22. Expand first, then look for a shortcut. 23 = 2 x 2 x 2. 22 = 2 x 2. Toge…
… repeated product of the inner power. Multiply and divide laws for the same base. Mathematics 1.3 Indices and Logarithms (23)2 means 23 used as a factor twice: 23 x 23. From the multiplication law that is 23+3 = 26. Addi…
…alis: OH-(aq). Bases include insoluble oxides. Indicators report those ions. UI classifies strong/weak. pH is logarithmic. Strength ≠ concentration. Three reactions: metal → H2; carbonate → CO2; base → water. Neutralisat…
… that follow from it. Multiplication and division of whole numbers. Nothing else. Mathematics 1.2 Indices and Logarithms Writing 2 x 2 x 2 x 2 x 2 is tedious. Writing 2 5 says the same thing in two symbols. That is all a…
… by matching powers, and solve for a base while keeping the base positive and not equal to 1. Index form of a logarithm, and powers of 2, 3, 4 and 5. Mathematics 1.4 Logarithms II Sometimes the unknown is the power, and …
… a negative number. The laws of indices from the first lesson of this sub-strand. Mathematics 1.2 Indices and Logarithms The first lesson stated a0 = 1 and a-n = 1/an. Both look like extra rules. They are not. They are w…
… is itself. Generate a 0 from the division law. Division law a m / a n = a (m-n). Mathematics 1.3 Indices and Logarithms Divide a power by itself: 23 / 23 = 8 / 8 = 1. The division law says 23-3 = 20. So 20 = 1. The same…
Mathematics Numbers in index form Laws of indices Powers of 10 to common logarithms express numbers in index form in different situations generate the laws of indices in different situations apply the laws of indices in …
Sub-strand
4.2 Single Stage Bipolar Junction Transistor (BJT) Amplifier
Electrical Technology · Grade 11
…ircuits. Physics: semiconductors, p-n junctions and the flow of charge carriers in a transistor. Mathematics: logarithms when expressing gain in decibels, and substitution in the gain formulae. Electrical Installation: s…
Rewrite each index statement in logarithm form: 1. 4 3 = 64 2. 10 5 = 100 000 3. 2 6 = 64 Introducing logarithms
…g 5.83 = 0.7657. Write log 58.3 and log 0.00583. 4. Why is log of a negative number not a real number? Common logarithms
Find the value of each: 1. log 2 32 2. log 10 0.01 3. log 7 1 Introducing logarithms
… 5 of x, plus log base 5 of (x - 4), equals 1. 3. Why is the negative candidate in question 2 not a solution? Logarithmic equations