#How to solve for n 1553*0.96^n<500

31 messages · Page 1 of 1 (latest)

tardy karma
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It's an inéquation
1553*0.96^n<500

But I could divide by 1553 and log base 0.96
But that's not always an option

If possible id like an explanation of how to use ln and logs here to solve for it

undone turretBOT
#
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undone turretBOT
faint aurora
#

doesn't have to be 0.96

tardy karma
#

How so can you détail the formulas and explain?

faint aurora
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use the property of logarithms

tardy karma
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I don't understand that property

faint aurora
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you can see on the third one

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if you take the log of a power

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the power becomes the coefficient

tardy karma
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Okay do I need to do something else to the other side of the inéquation? Like the 500, do I need to apply a log to it

faint aurora
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Yes

tardy karma
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Why

faint aurora
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because you apply log to both sides

tardy karma
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But that's the part where I'm stuck, if logx^n = nlogx then I can't I just replace the left side by it

faint aurora
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Yes?

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that's a property of logaithms

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But that's if you already divided both sides by 1553

tardy karma
# faint aurora that's a property of logaithms

I don't understand here's my logic I divide both sides by 1553

0.96^n=500/1553
I apply the property :
nlog(0.96) = 500/1553

Since they're both equal
And I divide by it
n= 500/1553/log(0.96)

faint aurora
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you can't just apply it to one side because then it's not equal

tardy karma
#

If i have sqrt(x^2) = 500 then I can just say x=500

faint aurora
tardy karma
faint aurora
#

you cannot use the property

tardy karma
#

Oh I see it's like we're transforming both sides

faint aurora
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Yes

undone turretBOT
#

@tardy karma

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