The discussion centers on the equivalence of two logarithmic expressions: 9 * ln | sqrt(4+x^2)/2 + x/2 | and 9 * ln | sqrt(4+x^2) + x |. It is established that these expressions are not equivalent in value for all x, but they share the same derivative due to the properties of logarithmic differentiation. The key insight is that ln(f(x)/2) can be rewritten as ln(f(x)) - ln(2), where the derivative of ln(2) is zero, thus confirming their derivative equivalence.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone interested in understanding logarithmic expressions and their derivatives.
whatlifeforme said:Homework Statement
how are these two problems equivalent?
Homework Equations
9 * ln | sqrt(4+x^2)/2 + x/2 | --->> = 9 * ln | sqrt(4+x^2) + x|
The Attempt at a Solution
i assume this has something to do with log rules.