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Extraneous Solutions and Domain Restrictions When solving logarithmic equations, extraneous solutions may arise. These are solutions that do not satisfy the domain of the original logarithmic expression. Remember: The domain of a logarithmic function \(\log_{b}{x}\) is \(x > 0\). Check all solutions to ensure they are within the domain.
We’ll break down the concept into bite-sized, manageable pieces, providing you with simple logarithm examples complete with step-by-step solutions. So, grab your calculator, and let’s demystify logarithms together!
Solution : log 2 (x + 3) + log 2 (x - 3) = 4. Use the fundamental law of logarithm. log 2 [(x + 3)(x - 3)] = 4. Convert to exponential form. (x + 3)(x - 3) = 2 4. x 2 - 3 2 = 16. x 2 - 9 = 16. x 2 = 25. √x 2 = √25. x = ± 5. x = -5 or 5. But, x = -5 will not work with the given equation. Because, x = -5 makes the arguments negative in the ...
Logarithm is another way of writing exponent. The problems that cannot be solved using only exponents can be solved using logs. Learn more about logarithms and rules to work on them in detail.
The logarithm of a number is the power or exponent by which another value must be raised to produce an equivalent value of the given number. The concept of logarithms was introduced in the early 17th century by John Napier – a Scottish mathematician.
In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. So the logarithm is 3. How to Write it. We write it like this: log2(8) = 3. So these two things are the same:
Math Article. Logarithms. In Mathematics, logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2. Hence, we can conclude that, Logb x = n or bn = x.
