So are you saying you gotJan Hill said:Homework Statement
y = log base 3 e^2x
Homework Equations
The Attempt at a Solution
I got y' = 2e^2x divided by e^2xln3
is this right?
Sorry for the pathetic way of presenting this. I haven't been able to use the lancet program for proper ways to write mathematical stuff
A logarithm derivative is a mathematical concept used to find the rate of change of a logarithmic function. It is denoted as dy/dx and is the inverse of the natural logarithm function.
To solve for y in this equation, you can use the property that log base a b = log base c b / log base c a. In this case, we can write the equation as y = (ln e^2x) / (ln 3) = 2x / (ln 3). This can also be written as y = 2x / ln 3.
The homework equations for solving logarithm derivatives include the chain rule, product rule, quotient rule, and power rule. These are used to find the derivative of a logarithmic function, just like in other types of derivative problems.
The chain rule can be used to solve logarithm derivatives by first rewriting the function as a composite function. Then, you can apply the chain rule, which states that the derivative of f(g(x)) = f'(g(x)) * g'(x). In the case of logarithmic functions, the inner function g(x) will be the argument of the logarithm, and the outer function f(x) will be the logarithm itself.
The solution to this equation is y = 2x / ln 3. This can also be written as y = log base 3 e^2x = 2x / ln 3. Alternatively, you can also write it in exponential form as e^y = 3^(2x), where y = 2x / ln 3.