Wiz14 said:The Following is defined,
log2004(log2003(log2002(log2001x)))
where x > c, what is c?
Answer is 2001^2002, but how to obtain it?
I do not know much about logs as I am only in precalculus.
A logarithm is the inverse function of an exponential. In other words, it helps us solve for the exponent in an exponential equation. On the AMC, logarithms are often used to simplify complicated expressions or equations, making them easier to solve.
The domain of a logarithmic function is all positive real numbers, since the input (or x-value) in an exponential equation must be greater than 0. The range, or output values, of a logarithmic function are all real numbers.
Some important properties of logarithms include the product rule, quotient rule, and power rule. These properties allow us to manipulate logarithmic expressions and make them easier to solve.
When solving exponential equations on the AMC, we can use logarithms to isolate the variable in the exponent and solve for it. We can also use logarithms to rewrite complicated expressions in a simpler form, making them easier to solve.
Some common mistakes to avoid when solving logarithmic problems on the AMC include forgetting to use parentheses when plugging in values, making arithmetic errors when simplifying logarithmic expressions, and forgetting to check for extraneous solutions. It is important to carefully check your work and be mindful of the properties of logarithms to avoid these mistakes.