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How do we decide what is the correct way to solve a logarithmic problem? The key is to look at the problem and decide if the problem contains only logarithms or if the problem has terms without logarithms.
After reading this text and / or viewing the video tutorial on this topic you should be able to: explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms.
A logarithm is just an index. We use log as an abbreviation for the word logarithm. To find the value of a logarithm we need to solve an exponential equation. Example (a) The solution of 2x = 8 is x = 3. We can write this in logarithm notation as log 2 8 = 3 ‘log of 8 to base 2 is 3’ (b) x = 5 is the solution of 2x = 32.
Solving Logarithmic Equations (Word Problems) Example 1. INVESTMENT Mr. and Mrs. Mitchell are saving for their daughter’s college education. They invest $10,000 in an account that pays 4.5% interest compounded continuously with the goal to have twice that amount in the account in ten years. a.
Every exponential function of the form f (x) bx, where b is a positive real number. =. other than 1, has an inverse function that you can denote by g(x) = logb x. This inverse function is called a logarithmic function with base b.
Logarithms make a lot of people anxious. A lot of this has to do with the way they're often taught in high school and secondary school: by memorizing all the proper steps, without imparting much deeper meaning. For example, maybe you were once taught to solve problems like this: log7 49 = ?
To solve equations which involve logarithms or exponentials we need to be aware of the basic laws which govern both of these mathematical concepts. We illustrate by considering some examples.
