SOLUTION: Solve the equation by rewriting the exponential expressions using the indicated logarithm. e^4x = 19 using the natural log 60^e−0.12t = 10 using the natural log *Kno

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Question 1129238: Solve the equation by rewriting the exponential expressions using the indicated logarithm.
e^4x = 19 using the natural log
60^e−0.12t = 10 using the natural log
*Knowing that the natural log base is 10 the answers that I came up with was: log10=19, but I don't know where the 4 is suppose to go. The same confusion goes for the second one, I thought the equation should be set up as log10=10, but I don't know where 60 and e^-0.12t goes. Can someone explain how to properly set up the equation? Thanks.
Found 3 solutions by Alan3354, ankor@dixie-net.com, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Solve the equation by rewriting the exponential expressions using the indicated logarithm.
e^4x = 19 using the natural log
Is the exponent 4? Or 4x?
-------------
60^e-0.12t = 10
Is the exponent -0.12 ?
Or -0.12t ?
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Solve the equation by rewriting the exponential expressions using the indicated logarithm.
:
the natural log base is not 10, it's e, base ten is the "common log"
:
assuming
using the natural log
the log equiv of exponents
4x*ln(e) = ln(19)
the ln of e = 1, therefore
4x = ln(19)
4x = 2.4999
x =
x = .7361
:


using the natural logs
e*ln(60) = ln(12t + 10)
using calc: find e*ln(60)
11.13 = ln(12t+10)
find the e^x of both sides
68186.37 = 12t + 10
subtract 10 from both sides
68176.37 = 12
t =
t = 5681.36
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!
Solve the equation by rewriting the exponential expressions using the indicated logarithm.
e^4x = 19 using the natural log
60^e−0.12t = 10 using the natural log
*Knowing that the natural log base is 10 the answers that I came up with was: log10=19, but I don't know where the 4 is suppose to go. The same confusion goes for the second one, I thought the equation should be set up as log10=10, but I don't know where 60 and e^-0.12t goes. Can someone explain how to properly set up the equation? Thanks. 
a)  If it's , then:

 ----- Converting to NATURAL LOGARITHMIC (ln) form





b)  If it's , then:

 ----- Taking the NATURAL LOG (ln) of each side











OR



b)  If it's , then you DO NOT NEED to use REGULAR or NATURAL LOGS to solve. Do as follows:





That's ALL!! 

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