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Rewrite as an exponential equation_ log₂ 27=3

Rewrite as an exponential equation_ log₂ 27=3

Calculus: Early Transcendentals
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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Hello, sorry if this is a repeat, seems like most of my questions do not go through on the first try.

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**Rewriting Logarithmic Equations as Exponential Equations** In mathematics, we often need to convert equations from logarithmic form to exponential form to simplify or solve them. Let's look at the following example: **Given Logarithmic Equation:** \[ \log_3 27 = 3 \] **Objective:** Rewrite this logarithmic equation as an exponential equation. **Step-by-Step Solution:** 1. **Identify the components of the logarithmic equation:** - The base \( 3 \) - The result \( 27 \) - The exponent \( 3 \) 2. **Understand the relationship:** A logarithmic statement \( \log_b a = c \) means that \( b \) raised to the power of \( c \) equals \( a \). 3. **Rewrite the equation in exponential form:** \[ 3^3 = 27 \] Therefore, the logarithmic equation \( \log_3 27 = 3 \) can be rewritten as the exponential equation \( 3^3 = 27 \). This shows the equivalent statement in exponential terms, confirming that when 3 is raised to the power of 3, the result is indeed 27.
Transcribed Image Text:**Rewriting Logarithmic Equations as Exponential Equations** In mathematics, we often need to convert equations from logarithmic form to exponential form to simplify or solve them. Let's look at the following example: **Given Logarithmic Equation:** \[ \log_3 27 = 3 \] **Objective:** Rewrite this logarithmic equation as an exponential equation. **Step-by-Step Solution:** 1. **Identify the components of the logarithmic equation:** - The base \( 3 \) - The result \( 27 \) - The exponent \( 3 \) 2. **Understand the relationship:** A logarithmic statement \( \log_b a = c \) means that \( b \) raised to the power of \( c \) equals \( a \). 3. **Rewrite the equation in exponential form:** \[ 3^3 = 27 \] Therefore, the logarithmic equation \( \log_3 27 = 3 \) can be rewritten as the exponential equation \( 3^3 = 27 \). This shows the equivalent statement in exponential terms, confirming that when 3 is raised to the power of 3, the result is indeed 27.
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