How Do Logarithms Solve Real-World Problems?

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The discussion revolves around the application of logarithms in various real-world contexts, including equations involving exponential decay, pH calculations, and earthquake magnitudes. Participants explore how logarithmic functions can be used to solve these problems.

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Approaches and Questions Raised

  • Participants attempt to solve equations involving logarithms and exponentials, questioning their calculations and interpretations of the problems. Some raise concerns about the accuracy of initial evaluations and suggest clarifying assumptions or definitions, such as the meaning of variables in the Richter scale equation.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning each other's reasoning. Some guidance has been offered regarding the interpretation of logarithmic equations and the need for clarity in problem setup. Multiple interpretations of the equations are being explored.

Contextual Notes

There are indications of potential misunderstandings regarding the notation used in the equations, particularly in the context of the Richter scale and the definitions of variables in Newton's law of cooling. Participants are encouraged to clarify their work and assumptions.

KrimsonB
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10^ x+3 = 6^2x ?

after i take the log of both sides and evaluating i end up getting -x = -2.22

a car engine runs at a temperature of 190 f when the engine is turned off it cools according to Newtons law of cooling with constant k = 0.0341, where the time is measure in minutes. find the time needed for the engine to cool 90f if the surrounding temp is 60f
T(t)=Ts+Doe^-kt

the ph of lime juice IS 1.9 FIND THE HYDROGEN ION CONCENTRATION

PH= -LOG [H+]

IF ONE EARTHQUAKE HAS A MAGNITUDE OF 6.5 ON THE RICHTER SCALE, WHAT IS THE MAGNITUDE OF ANOTHER QUAKE THAT IS 35 TIMES AS INTENSE?

M=LOG(I\S)

x^2e ^2x + 2xe^2x = 8e^2x
 
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KrimsonB said:
10^ x+3 = 6^2x ?

after i take the log of both sides and evaluating i end up getting -x = -2.22

I think this may be wrong, you may need to do it over, unless I typed it in my calculator incorrectly.

KrimsonB said:
a car engine runs at a temperature of 190 f when the engine is turned off it cools according to Newtons law of cooling with constant k = 0.0341, where the time is measure in minutes. find the time needed for the engine to cool 90f if the surrounding temp is 60f
T(t)=Ts+Doe^-kt

you need to post your work for this. Start by finding the value of D0

KrimsonB said:
the ph of lime juice IS 1.9 FIND THE HYDROGEN ION CONCENTRATION

PH= -LOG [H+]

So you know that 1.9 = -lg[H+], how would you go about taking anti-logs?

KrimsonB said:
IF ONE EARTHQUAKE HAS A MAGNITUDE OF 6.5 ON THE RICHTER SCALE, WHAT IS THE MAGNITUDE OF ANOTHER QUAKE THAT IS 35 TIMES AS INTENSE?

M=LOG(I\S)[/QUOTE]

I am not sure what I and S are. I assume M meant magnitude.

KrimsonB said:
x^2e ^2x + 2xe^2x = 8e^2x

You can easily solve for x here since e2x is common in every term and will cancel out.
 
KrimsonB said:
10^ x+3 = 6^2x ?

after i take the log of both sides and evaluating i end up getting -x = -2.22
I assume you mean 10^(x+3)= 6^(2x).
Taking logarithms of both sides, x+ 3= 2x(log(6))
(log(6)-1)x= 3.

x clearly is positive.

a car engine runs at a temperature of 190 f when the engine is turned off it cools according to Newtons law of cooling with constant k = 0.0341, where the time is measure in minutes. find the time needed for the engine to cool 90f if the surrounding temp is 60f
T(t)=Ts+Doe^-kt
Well, what do Ts and Do represent?

the ph of lime juice IS 1.9 FIND THE HYDROGEN ION CONCENTRATION

PH= -LOG [H+]
So log[H+]= -PH. [H+]= exp(-PH)

IF ONE EARTHQUAKE HAS A MAGNITUDE OF 6.5 ON THE RICHTER SCALE, WHAT IS THE MAGNITUDE OF ANOTHER QUAKE THAT IS 35 TIMES AS INTENSE?

M=LOG(I\S)
Log(35)

x^2e ^2x + 2xe^2x = 8e^2x
What is the problem? To solve for x? What do you get if you divide the entire equation by e^(2x)?
 
The pH is defined thus: pH = -log (H+ conc.) = log (1/H+ conc.), where log is base ten or common logarithms. Therefore [H+] = 10^(-pH).
 
About 10^ x+3 = 6^2x: if we parse this using the usual rules (exponentiation takes precedence over multiplication), you have written
10^x + 3 = 36*x. If your really mean 10^x + 3 = 6^(2x), you need to include brackets.

RGV