Math Problem Statement

The coordinates of a point on the graph of the indicated​ function, shown to the​ right, are displayed at the bottom of the screen.

Write the logarithmic and exponential equations associated with the display.

-110 -3    3xY1=ln(X)

nothing

Upper X equals 2.95X=2.95

Upper Y equals 1.0818052Y=1.0818052

g left parenthesis x right parenthesis equals ln xg(x)=ln x

A coordinate system has a horizontal x-axis labeled from negative 1 to 10 in increments of 1 and a vertical y1=ln(x)-axis labeled from negative 3 to 3 in increments of 2. From right to left, a curve labeled g(x) = ln x falls at an increasing rate, passing through the points (10, 2.3), the plotted point marked with an X at (3, 1.1), and (1, 0). As x approaches 0 from the right, the curve approaches negative infinity. At the bottom of the screen X=2.95 and Y=1.0818052 are labeled. All coordinates are approximate.

Question content area bottom

Part 1

Write the logarithmic equation.

The logarithmic equation is

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Solution

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Math Problem Analysis

Mathematical Concepts

Logarithmic Functions
Exponential Functions
Natural Logarithms

Formulas

g(x) = ln(x)
Y = ln(X)
Inverse: e^Y = X

Theorems

Logarithmic and Exponential Relationship
Inverse Function Theorem

Suitable Grade Level

Grades 10-12