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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.
Sometimes you need to write an expression as a single logarithm. Use the rules to work backwards. Example 6 Write 2 log 3 x + log 3 y as a single logarithm log 3 x 2 + log 3 y Use the Power Rule for Logarithms to move the 2 in 2 log 3 x to the exponent of x = log 3 x 2y Use the Product Rule for Logarithms. The answer is 2log 3 x y Example 7 ...
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 ...
Detailed step by step solutions to your Write as single logarithm problems with our math solver and online calculator.
on your calculator, you will getclose to the value of e. Like . π, e is an irrational number. Throughout this section, we will use e in expressions of the form: • e x, which is called an exponential to the base e; • log e x, which is called a logarithm to the base . This is also known as the e natural logarithm of x, and is often written ...
Find the unknown in each of the following equations. Show all your work. 2. For each of the following: Write the expression as a single logarithm using the rules of logarithms. Evaluate to a single number or estimate the value of the expression. log. 3.Solve each equation. Show all your work.
LOGARITHMS PRACTICE SIMPLIFYING EXPRESSIONS. single logarithm. log 2 7 + log 2 2. log 2 20 − log 2 4. 3log 5 2 + log 5 8. 2log 6 8 − 5log 6 2. log 10 8 + log 10 5 − log 10 0.5. log 2 14 , log 2 5 , log 5 64 , log 6 2 , log 10 80. single logarithm.
