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Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y = ln x ³

User Impo
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Final answer:

To find the equation of the tangent line to the graph of the logarithmic function at the point (1, 0), we first see the function's derivative and substitute the x-coordinate value of the given moment into the derivative. Then, we use the point-slope form to determine the equation of the tangent line. The equation of the tangent line to the graph of the logarithmic function at the point (1, 0) is y = 3x - 3.

Step-by-step explanation:

The derivative of ln(x³) is 3/x. Next, we substitute the x-coordinate value of the given point (1) into the derivative to find the slope of the tangent line. The pitch is 3/1 = 3.

Since the tangent line passes through the point (1, 0), we can use the point-slope form of a linear equation, which states that y - y₁ = m(x - x₁). Substituting the values, we get y - 0 = 3(x - 1). Simplifying, we have y = 3x - 3.

Therefore, the tangent line's equation to the logarithmic function graph at the point (1, 0) is y = 3x - 3.

User Vendettamit
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