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1. Write the equation log2439 = in exponential form. [A] 2435-9 243 [C] =9 [B] 95-243 [D] 9 - 243 2. Write the equation log₁81== in 5 exponential form. [A] 81-243 [C] 2433-81 243 [B] (3) [D] 81³-243 =81

1. Write the equation log2439 = in exponential form. [A] 2435-9 243 [C] =9 [B] 95-243 [D] 9 - 243 2. Write the equation log₁81== in 5 exponential form. [A] 81-243 [C] 2433-81 243 [B] (3) [D] 81³-243 =81

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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Answer multiple questions 1-3. Answer short questions 4-5
Below is a transcription of the content: --- 1. Write the equation \( \log_{243} 9 = \frac{2}{5} \) in exponential form. - [A] \( 243^{\frac{2}{5}} = 9 \) - [B] \( 9^{\frac{2}{5}} = 243 \) - [C] \( \left(\frac{2}{5}\right)^{243} = 9 \) - [D] \( 9^{\frac{5}{2}} = 243 \) 2. Write the equation \( \log_{243} 81 = \frac{4}{5} \) in exponential form. - [A] \( 81^{\frac{5}{4}} = 243 \) - [B] \( \left(\frac{4}{5}\right)^{243} = 81 \) - [C] \( 243^{\frac{4}{5}} = 81 \) - [D] \( 81^{\frac{4}{5}} = 243 \) 3. Write the equation \( \log_{16} 8 = \frac{3}{4} \) in exponential form. - [A] \( 16^{\frac{3}{4}} = 8 \) - [B] \( 8^{\frac{3}{4}} = 16 \) - [C] \( 8^{4} = 16 \) - [D] \( \left(\frac{3}{4}\right)^{16} = 8 \) 4. Write the equation \( \log_{16} 64 = \frac{3}{2} \) in exponential form. 5. Write the equation \( \log_{1024} 256 = \frac{4}{5} \) in exponential form. --- Note: The equations are asking to convert logarithmic forms to exponential expressions with options provided in multiple-choice format for the initial few questions.
Transcribed Image Text:Below is a transcription of the content: --- 1. Write the equation \( \log_{243} 9 = \frac{2}{5} \) in exponential form. - [A] \( 243^{\frac{2}{5}} = 9 \) - [B] \( 9^{\frac{2}{5}} = 243 \) - [C] \( \left(\frac{2}{5}\right)^{243} = 9 \) - [D] \( 9^{\frac{5}{2}} = 243 \) 2. Write the equation \( \log_{243} 81 = \frac{4}{5} \) in exponential form. - [A] \( 81^{\frac{5}{4}} = 243 \) - [B] \( \left(\frac{4}{5}\right)^{243} = 81 \) - [C] \( 243^{\frac{4}{5}} = 81 \) - [D] \( 81^{\frac{4}{5}} = 243 \) 3. Write the equation \( \log_{16} 8 = \frac{3}{4} \) in exponential form. - [A] \( 16^{\frac{3}{4}} = 8 \) - [B] \( 8^{\frac{3}{4}} = 16 \) - [C] \( 8^{4} = 16 \) - [D] \( \left(\frac{3}{4}\right)^{16} = 8 \) 4. Write the equation \( \log_{16} 64 = \frac{3}{2} \) in exponential form. 5. Write the equation \( \log_{1024} 256 = \frac{4}{5} \) in exponential form. --- Note: The equations are asking to convert logarithmic forms to exponential expressions with options provided in multiple-choice format for the initial few questions.
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\log _{243}\left(9\right)=\frac{2}{5}

write both sides as an exponent of 243

243^{\log _{243}\left(9\right)}=243^{\frac{2}{5}}

use the log rule \:a^{\log _a\left(b\right)}=b

9=243^{\frac{2}{5}}

switch both sides

{\color{Red} 243^{\frac{2}{5}}=9}..................option A

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