#Logarithms Problem

50 messages · Page 1 of 1 (latest)

raven jacinth
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The answer is a = -20, b = -40, I believe. But I don't know how to solve this.

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dark roost
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i would suggest u use the base change rule that is

$log_{a}b = \frac{log_{d}b}{log_{d}a}$

raw matrixBOT
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racism | #GTFOanemia

raven jacinth
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what do i do after that

dark roost
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sry had to go somewhere

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im back

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uh

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so

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the solutions u mentioned dont work

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i think

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they shouldnt lets check

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,w -20 + (-40)log_(4)7 + 60 log_(8)14

dark roost
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oh they do

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which means

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after applying base change u arrive here:

raven jacinth
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i got the solutions using desmos

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but i need to solve it algebraically

dark roost
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$a + b \frac{\log 7}{\log 4} + 60 \frac{\log 14}{\log 8} = 0$

raw matrixBOT
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racism | #GTFOanemia

dark roost
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now take log 8 as a common base

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and note that $\frac{3}{2} \log 4 = \log 8$

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because of the power property of logs

raw matrixBOT
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racism | #GTFOanemia

raven jacinth
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ok

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4^3/2 = 8 ye right

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ok

dark roost
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Yes

raven jacinth
dark roost
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No u needed to do it to log4

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To get a common denominator

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This would work too but it does the same thing

raven jacinth
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so what after this

dark roost
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Get a common denominator

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Then equate numerator to 0

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did u do it @raven jacinth

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$a + b \frac{\frac{3}{2} \log 7}{\log 8} + 60 \frac{\log 14}{\log 8} = 0$

raw matrixBOT
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racism | #GTFOanemia

dark roost
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$\frac{a \log 8}{\log 8} + b \frac{\frac{3}{2} \log 7}{\log 8} + 60 \frac{\log 14}{\log 8} = 0$

raw matrixBOT
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racism | #GTFOanemia

dark roost
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$a \log 8 + b \log 7^\frac{3}{2} + 60 \log 14 = 0$

raw matrixBOT
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racism | #GTFOanemia

dark roost
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@raven jacinth can you continue?

raven jacinth
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yes

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ive done it

dark roost
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ok