Thank you for visiting Amir does a good deed for each of his 5 friends They then each do one good deed for 5 friends Write an exponential equation. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure! Let's go through the solution step by step.
We are given that Amir does a good deed for each of his 5 friends. They then each do a good deed for their 5 friends, and this process continues iteratively.
We want to find an exponential equation that represents the number of iterations, [tex]\( x \)[/tex], to reach a total of 625 good deeds. Then, we will convert this exponential equation into its logarithmic form.
### Step-by-Step Solution:
1. Identify the Initial Scenario:
- Amir starts by performing deeds for his 5 friends. This is our starting point.
- Each of these 5 friends also does the same for their 5 friends, and so forth.
2. Exponential Growth Concept:
- The number of good deeds grows exponentially. Initially, Amir’s good deeds are represented by [tex]\( 5^0 \)[/tex]. The exponent represents the iteration number.
- After 1 iteration, there are [tex]\( 5^1 \)[/tex] good deeds.
- After 2 iterations, there are [tex]\( 5^2 \)[/tex] good deeds.
- This pattern continues such that the total good deeds after [tex]\( x \)[/tex] iterations can be represented by [tex]\( 5^x \)[/tex].
3. Formulating the Equation:
- We are given that after [tex]\( x \)[/tex] iterations, the total number of good deeds is 625.
- Hence, the exponential equation representing this scenario is:
[tex]\[
5^x = 625
\][/tex]
4. Converting to Logarithmic Form:
- By definition, an exponential equation [tex]\( a^b = c \)[/tex] can be converted to logarithmic form as [tex]\( \log_a c = b \)[/tex].
- Applying this to our equation [tex]\( 5^x = 625 \)[/tex]:
[tex]\[
\log_5 625 = x
\][/tex]
Therefore, the correct exponential equation and its corresponding logarithmic form are:
[tex]\[ 5^x = 625 \quad \text{and} \quad \log_5 625 = x \][/tex]
From the provided options, this matches with:
### A. [tex]\( 5^x = 625 \; ; \; \log_5 625 = x \)[/tex]
So, the correct answer is:
A. [tex]\( 5^x=625 ; \log_5 625=x \)[/tex]
We are given that Amir does a good deed for each of his 5 friends. They then each do a good deed for their 5 friends, and this process continues iteratively.
We want to find an exponential equation that represents the number of iterations, [tex]\( x \)[/tex], to reach a total of 625 good deeds. Then, we will convert this exponential equation into its logarithmic form.
### Step-by-Step Solution:
1. Identify the Initial Scenario:
- Amir starts by performing deeds for his 5 friends. This is our starting point.
- Each of these 5 friends also does the same for their 5 friends, and so forth.
2. Exponential Growth Concept:
- The number of good deeds grows exponentially. Initially, Amir’s good deeds are represented by [tex]\( 5^0 \)[/tex]. The exponent represents the iteration number.
- After 1 iteration, there are [tex]\( 5^1 \)[/tex] good deeds.
- After 2 iterations, there are [tex]\( 5^2 \)[/tex] good deeds.
- This pattern continues such that the total good deeds after [tex]\( x \)[/tex] iterations can be represented by [tex]\( 5^x \)[/tex].
3. Formulating the Equation:
- We are given that after [tex]\( x \)[/tex] iterations, the total number of good deeds is 625.
- Hence, the exponential equation representing this scenario is:
[tex]\[
5^x = 625
\][/tex]
4. Converting to Logarithmic Form:
- By definition, an exponential equation [tex]\( a^b = c \)[/tex] can be converted to logarithmic form as [tex]\( \log_a c = b \)[/tex].
- Applying this to our equation [tex]\( 5^x = 625 \)[/tex]:
[tex]\[
\log_5 625 = x
\][/tex]
Therefore, the correct exponential equation and its corresponding logarithmic form are:
[tex]\[ 5^x = 625 \quad \text{and} \quad \log_5 625 = x \][/tex]
From the provided options, this matches with:
### A. [tex]\( 5^x = 625 \; ; \; \log_5 625 = x \)[/tex]
So, the correct answer is:
A. [tex]\( 5^x=625 ; \log_5 625=x \)[/tex]
Thank you for reading the article Amir does a good deed for each of his 5 friends They then each do one good deed for 5 friends Write an exponential equation. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
