### 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
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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.

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Write an equation for the transformed logarithm shown below, that passes through (0,0) and (2,-3 -5 -4 -3 -2 -1 -2 t-4 f(x) = Preview syntax error praic expression [more..]

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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### 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.

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Please help with with this thanks!
How many of the following characteristics can two different logarithmic functions share, while still remaining different? •Domain Range •y-intercept Intervals of increase or decrease Decide how many key characteristics and explain your position with examples.
Write an equation for the transformed logarithm shown below, that passes through (3,0) and (0,3) -5 -4 -3 -2 -1 f(x) = 4 Ani 3 2 I -1 23 -4 5 12 =1