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#1 2006-10-01 12:38:05

runlemmingsrun1
Guest

exponents

Please convert the equation into exponential form:

   X=log4Y

   Thanks

#2 2006-10-01 13:04:45

polylog
Member
Registered: 2006-09-28
Posts: 162

Re: exponents

Recall that the base-4 logarithm with argument y is the function that gives you "what number 4 needs to be raised to, in order to get y", and the equation says: "this number which 4 needs to be raised to, is x".   

Thus, this is the same as saying:  4^x = y.  Which is in exponential form.


If you like a more algebraic method:

x = log4(y)

apply the change of base formula logb(t) = ln(t)/ln(b):

x = ln(y)/ln(4)

x*ln(4) = ln(y)

recall that k*ln(t) = ln(t^k):

ln(4^x) = ln(y)

exponentiate both sides:

e^(ln(4^x)) = e^(ln(y))

4^x = y

Same thing. smile

The second method is better if you remember those formulas and it requires less thinking. smile

another way is to take the 'Antilog base 4 ' of both sides:

antilog4(x) = antilog4(log4(y))

4^x = y

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#3 2006-10-02 09:46:40

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: exponents

runlemmingsrun1 wrote:

Please convert the equation into exponential form:

   X=log4Y

   Thanks

X = log(4Y) is the same as 10^X = 4Y


Notice polylog and I have interpreted your problem in two different ways. Whoever interpreted it correctly offers the answer you seek.


You can shear a sheep many times but skin him only once.

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