Allison is solving the following equation for t: A = 5,000(1.1) A 5,000 log1.1 = (1.1) A 5,000 = t and wants to evaluate this expression for particular values of A, but doesn't have a calculator with a log1.1 button. What is an equivalent expression Allison can use to evaluate using the common log button on the calculator.
Allison is solving the following equation for t: A = 5,000(1.1) A 5,000 log1.1 = (1.1) A 5,000 = t and wants to evaluate this expression for particular values of A, but doesn't have a calculator with a log1.1 button. What is an equivalent expression Allison can use to evaluate using the common log button on the calculator.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![Allison is solving the following equation for \( t \):
\[
A = 5{,}000(1.1)^t
\]
Rearranging gives:
\[
\frac{A}{5{,}000} = (1.1)^t
\]
Taking the logarithm of both sides:
\[
\log_{1.1} \left(\frac{A}{5{,}000}\right) = t
\]
Allison wants to evaluate this expression for particular values of \( A \) but doesn't have a calculator with a \(\log_{1.1}\) button. She needs an equivalent expression using the common log button on the calculator:
Possible options are:
- \(\frac{\log \left(\frac{A}{5{,}000}\right)}{\log(10)}\)
- \(\frac{\log \left(\frac{A}{5{,}000}\right)}{\log(1.1)}\)
- \(\log \left(\frac{A}{5{,}000}\right) - \log(1.1)\)
The correct expression allows Allison to compute the value of \( t \) using common logarithms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3d4b5b-7c63-4562-84e8-65fa84143989%2F0cf37ba6-859c-4654-9ab6-1f3c48e850ba%2Fl6cegw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Allison is solving the following equation for \( t \):
\[
A = 5{,}000(1.1)^t
\]
Rearranging gives:
\[
\frac{A}{5{,}000} = (1.1)^t
\]
Taking the logarithm of both sides:
\[
\log_{1.1} \left(\frac{A}{5{,}000}\right) = t
\]
Allison wants to evaluate this expression for particular values of \( A \) but doesn't have a calculator with a \(\log_{1.1}\) button. She needs an equivalent expression using the common log button on the calculator:
Possible options are:
- \(\frac{\log \left(\frac{A}{5{,}000}\right)}{\log(10)}\)
- \(\frac{\log \left(\frac{A}{5{,}000}\right)}{\log(1.1)}\)
- \(\log \left(\frac{A}{5{,}000}\right) - \log(1.1)\)
The correct expression allows Allison to compute the value of \( t \) using common logarithms.
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