SOLUTION: For a specified real number, twice the log of the number that is two less than the specified number will equal the log of the number that is 8 less than 3 times the specified numbe

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Question 443682: For a specified real number, twice the log of the number that is two less than the specified number will equal the log of the number that is 8 less than 3 times the specified number.
what could the specified number possibly be?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
For a specified real number, twice the log of the number that is two less than the specified number will equal the log of the number that is 8 less than 3 times the specified number.
what could the specified number possibly be?
:
Let x = a specified number
:
Write an equation for statement, (commas help):
"twice the log of the number, that is two less than the specified number, will equal the log of the number, that is 8 less than 3 times the specified number."
:
2*log(x-2) = log(3x-8)
The exponent equiv
log((x-2)^2) = log(3x-8)
therefore
(x-2)^2 = 3x - 8
FOIL the left side:
x^2 - 4x + 4 = 3x - 8
x^2 - 4x - 3x + 4 + 8 = 0
x^2 - 7x + 12 = 0
Factors to
(x-4)(x-3) = 0
Two solutions as the specified number
x=4
x=3
:
:
Check solution x=4 in the original equation
2*log(4-2) = log(3(4)-8)
2*log(2) = log(4); confirms our solution
:
You can check the x=3 solution (remember log of 1 = 0)