#Logarithms

82 messages · Page 1 of 1 (latest)

orchid forgeBOT
iron parcel
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Well firstly we note that 2023=289*7

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I’m 90% sure you can compute each of the logs but i forget how

full moat
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is it a numerical answer

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or is it in terms of log

tulip mango
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The answer should be like 0.00079285... and
-0.00079285...

sharp mortar
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log rule problem

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uhh lets see

full moat
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wait wat?

full moat
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we have to find x rt?

sharp mortar
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no it definitely doesnt want that

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it wants you to use log rules

full moat
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wat?

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i dint understand sory

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i got a weird answer that seems to work

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i have to plug in the originial eqn and check

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i got this

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and it works

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like if u plug the non decimal part (943) in the eqn u get the correct answer up to 3 decimals

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so keeping all the decimals

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i think it is the correct answer

tulip mango
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Okay...lemme check it once more

full moat
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k

sharp mortar
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the question definitely wants this in log form though

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you have to manipulate it using log rules to get the result

tulip mango
full moat
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i got

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2023^(sqrt(1-log 7 base 2023 *log 289 base 2023))

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nvm

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so ya

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i think the 2nd root is

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the exponent being negative

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sqrt(1-log 7 base 2023 *log 289 base 2023

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all this

sharp mortar
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not too sure how to get this into log form tbh

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ive been trying different rules for a while now

full moat
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ok so

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do u know

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log a + log b

full moat
sharp mortar
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yeah

sharp mortar
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dont believe this is right tho

floral violet
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yeah so basically

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you want to first apply log_a(x)=ln(x)/ln(a)

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then you notice that all the ln(2023) cancel

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apply the inverse and you're left with:

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ln(7x)ln(289x)=ln(2023x)

tawdry whale
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wow dude... finally something i know to do in this discord server :

floral violet
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use the fact ln(ab)=ln(a)+ln(b), and then solve for ln(x) like a quadratic equation

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oh wait

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you want the product of the solutions

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so then you just want to use vieta formula

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so you just need the coefficients of the quadratic formula and you're done 🙂

full moat
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ok so what i did was

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log a base b = 1/log b base a

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so

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flip the entire eqn

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now

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u have log 7x base 2023

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so

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it is equal to log 7 base 2023 + log x base 2023

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do that to all terms

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now u have quadratic in log x

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expand it

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u get

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(log x base 2023)^2 = 1-log 7 base 2023 * log 289 base 2023

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ig

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someone pls verify this

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i checked my method and im quite sure im rght

floral violet
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I wrote that

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just before you

full moat
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sorry

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i got confused with ln()

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but ya ok tq

sharp mortar
soft sage
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1 as the product is what I got

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kind of messy to get there but you can double check it on wolfram alpha

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what class was the problem for?