How Do Logarithms Solve Real-World Problems?

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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