How Do Logarithms Solve Real-World Problems?

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In summary: Newtons law of cooling with a constant k of 0.0341. Find the time needed for the engine to cool 90 degrees if the surrounding temperature is 60 degrees.
  • #1
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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  • #2
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.
 
  • #3
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)?
 
  • #4
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).
 
  • #5
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
 

Related to How Do Logarithms Solve Real-World Problems?

1. What are logarithms and how are they used in word problems?

Logarithms are mathematical functions that represent the inverse of exponential functions. They are used to solve problems involving exponential growth or decay, such as population growth, compound interest, and radioactive decay.

2. How do I know when to use logarithms in a word problem?

You can use logarithms when the problem involves finding the unknown number in an exponential equation, or when the problem involves repeated multiplication or division. Look for keywords such as "growing at a constant rate" or "half-life" to determine if logarithms are needed.

3. What is the difference between common logarithms and natural logarithms?

Common logarithms, denoted as log base 10, use the base of 10 and are commonly used in everyday calculations. Natural logarithms, denoted as ln, use the base of e (approximately 2.718) and are often used in calculus and scientific calculations.

4. How do I solve word problems involving logarithms?

To solve word problems involving logarithms, first identify the unknown variable and write out the given information in an equation using logarithms. Then, use properties of logarithms, such as the power rule or product rule, to simplify the equation and solve for the unknown variable.

5. What are some real-life applications of logarithms?

Logarithms are used in various fields such as finance, biology, chemistry, and physics. They are commonly used to model population growth, calculate interest and depreciation, measure pH levels, and determine the half-life of radioactive substances.

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