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Simplify each of the following logarithmic expressions, giving the final answer as a number not involving a logarithm. a) log 24 log 32 2− b) log 96 3log 2 log 43 3 3− − c) 5 5 5 1 2 log 500 log log 10 5 + − d) 2log 54 log 0.25 4log 23 3 3− − e) 8log 2 log 4 3log 96 6 6− −( ) 3 , 1 , 3 , 6 , 6
14 sie 2024 · 📈 Discover the value of log 1 to 100 with detailed tables and charts in PDF format. Simplify your calculations with comprehensive guide!
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(a) Find a formula for the number of bacteria at time t. (b) Find the number of bacteria after one hour. (c) After how many minutes will there be 50 000 bacteria?
The following examples show how to expand logarithmic expressions using each of the rules above. Use the Power Rule for Logarithms. Since 7a is the product of 7 and a, you can write 7a as 7 • a. Use the Product Rule for Logarithms. 5 3 log = log511 – log53 Use the Quotient Rule for Logarithms.
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. We can write this using logarithms as log 2
base 10 and base e Logarithms to base 10, log 10, are often written simply as log without explicitly writing a base down. So if you see an expression like logx you can assume the base is 10. Your calculator will be pre-programmed to evaluate logarithms to base 10. Look for the button marked log. e, e
