Ln (2x^2-3x)^4 how to solve it. I did the steps but none of my answers are the choices
Solve it?
You mean what is the deriviative?
y=ln( u)
dy/dx=1/u * du/dx
so if u=(2x^2-3x)^4, then
du = 4( )^3 * (4x-3)
dy/dx=1/( )^4 * 4( )^3 * (4x-3)
=1/( ) * 4(4x-3)
But when I do it none of the answers are right
Really? According to whom?
Did You mean: [ln(2x^2-3x)]^4
OR
ln[(2x^2-3x)^4]
Go to:
wolframalpha dot com
When page be open in rectangle type your function and click option =
After few seconds you will see all about your function.
Then click option Derivative:Show steps.
When you see steps you click on down left angle in Derivative field and you can save solution as image.
To simplify the expression Ln(2x^2 - 3x)^4, let's break it down into steps:
1. Apply the power rule of logarithms: Ln(a^b) = b * Ln(a). This allows us to bring the exponent 4 in front as a coefficient:
4 * Ln(2x^2 - 3x)
2. Now, we need to simplify the expression inside the natural logarithm. We can factor out the common factor of x:
4 * Ln(x(2x - 3))
3. Applying the logarithmic property Ln(ab) = Ln(a) + Ln(b), we can split the logarithm into two separate logarithms:
4 * (Ln(x) + Ln(2x - 3))
4. Simplify the expression by distributing the coefficient of 4:
4 * Ln(x) + 4 * Ln(2x - 3)
Now, based on the choices you have, you can evaluate Ln(x) and Ln(2x - 3) for specific values of x, and then multiply by 4 to find the correct answer. Remember to check your calculations and ensure you haven't made any errors in evaluating the logarithms or simplifying the expression.