2 thoughts on “REMINDER: No Class today”

  1. Professor! This is Suim Kim.

    I am trying to solve Exponential Functions – Equations: Problem 7 on webwork

    (1.31)x=28

    but I am still struggling to solve it. It is a bit hard to not have any decimals. How do can I make it in an exact form with no approximations? I tried to multiply number 100 to each section but what I got is x= (log 2800)/(log 131) which is not an answer.

    I hope our class can talk about it!

    Thank you and I hope you stay healthy and safe.

  2. [latexpage]
    Hi Suim! Sure, I can help. You started with:
    $(1.31)^x=28$
    Take the log of both sides:
    $\log (1.31^x)=\log 28$
    and move the exponent to the front:
    $x \log 1.31 = \log 28$

    Unfortunately, we can’t get rid of the decimal by multiplying both sides by 100 — because the decimal is buried inside the $\log$, and multiplying $100 \log 1.31$ is not the same as $\log 131$.

    Instead, we will use the fact that 1.31 = 131/100, and substitute this in the left side:
    $x \log (131/100) = \log 28$
    Now get the $x$ by itself to obtain your answer.

    Hope this helps – let me know if you’re still stuck.

    All the best,
    Prof. Reitz

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