### Writing an Equation for a Transformed Logarithm**Problem Statement:**Write an equation for the transformed logarithm shown below that passes through the points \((0,0)\) and \((2,-3)\).**Graph Description:**The graph is a plot on a coordinate grid. The x-axis ranges from -5 to 5, and the y-axis ranges from -5 to 5. The graph features a blue curve representing a logarithmic function, which passes through the origin \((0,0)\) and the point \((2,-3)\).- The curve starts at the point \((0,0)\) and descends towards the point \((2,-3)\), showing a transformed logarithmic behavior. - The red dashed line at \(x = -1\) likely indicates a vertical asymptote, typical of logarithmic functions, if shifted.**Interactive Component:**There is an input box labeled \(f(x) =\) where users are prompted to "Enter an algebraic expression."### Additional Notes:- Ensure the entered equation reflects the transformations (translations and/or dilations) that align the curve with the given points.- The equation should be in logarithmic form, likely involving parameters that cause the curve to pass through the specified points.- Viewers can get assistance via a linked video resource.**Common Transformations for Logarithms:**- Horizontal shifts: \(f(x) = \log_b(x - h)\)- Vertical shifts: \(f(x) = \log_b(x) + k\)- Vertical stretching/compression: \(f(x) = a \cdot \log_b(x)\)Based on the passage through \((0,0)\) and \((2,-3)\), determine the specific transformations applied.

Name: ### Writing an Equation for a Transformed Logarithm**Problem Statemen
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: ### Writing an Equation for a Transformed Logarithm**Problem Statement:**Write an equation for the transformed logarithm shown below that passes through the points \((0,0)\) and \((2,-3)\).**Graph Description:**The graph is a plot on a coordinate gr

Given: The transformed graph of logarithm function which is passing through 0,0 and 2,-3 as, To find: Equation of function for which graph is given.Explanation: Consider the function as fx=alogex+c Since the curve is passing through 0,0 and 2,-3 Therefore f0=0, f2=-3 Putting x=0 in fx=alogex+c, f0=alogeb×0+c⇒0=alogec ∵f0=0⇒logec=0 ∵a≠0⇒c=1 Hence fx=alogex+1, Putting x=2 in fx=alogex+1, f2=aloge2+1⇒-3=aloge3 ∵f2=-3⇒a=-3loge3 Hence required function is fx=-3loge3logex+1. Answer: fx=-3loge3logex+1.