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We use can logarithms to solve exponential equations: The solution of ax = b is x = log a b For example, the solution of ex = 2 is x = log e 2. To find the value of this logarithm, we need to use a calculator: log e 2 = 0.6931. Note Logarithms were invented and used for solving exponential equations by the Scottish baron John Napier (1550 ...
•explain what is meant by a logarithm •state and use the laws of logarithms •solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second ...
The function f(x) = ax for 0 < a < 1 has a graph which is close to the x-axis for positive x and increases rapidly for decreasing negative x. For any value of a, the graph always passes through the point (0,1).
Question When the base changes from 10 to b, what is the logarithm of 1 ? Answer Since b0 D 1, logb 1 is always zero. To base b, the logarithm of bn is n: Negative powers are also needed. The number 10x is positive, but its exponent x can be negative. The first examples are 1=10 and 1=100, 1 which are the same as 10 and.
-Because an exponent will never have negative output (see above), a logarithm can never have negative input. -Because when you raise a number to the 0 power, you get 1, whenever, I repeat, whenever, you put 1 inside a logarithm, you get 0. In other words, 𝐥𝐨𝐠𝒃( )= .
logarithm of a number, all you have to do is count its digits. For example the number 83,176,000 has eight digits, and therefore its log must be between 7 and 8. And since it’s a large eight-digit number, the log is closer to 8 than 7. (In fact, the log of this number is approximately 7.92.) Here’s the graph of positive base-10 logarithms ...
• Reflection of graph of y = ax about the line y = x. The basic characteristics of the graph of f (x) = ax are shown below to illustrate the inverse relation between f (x) = ax and g(x) = log a x. • Domain: ( , ) • Range: (0, ) • y-intercept: (0, 1) • x-axis is a horizontal asymptote (ax → 0 as x→ ).
