SOLUTION: Use the one to one property to solve the equations for x
A) log 11=log (x^2+7)
B)e ^x^2-3=e^2x
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Question 1136697: Use the one to one property to solve the equations for x
A) log 11=log (x^2+7)
B)e ^x^2-3=e^2x
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
A)
...if log same then
±
B)
...if base same then exponents are same too
solutions: or
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a.)
log(11) = log(x^2 + 7)
this is true if and only if 11 = x^2 + 7
subtract 7 from both sides to get 4 = x^2.
solve for x to get x = plus or minus 2.
when x = plus or minus 2, x^2 is 4.
log(11) = log(x^2 + 7) becomes log(11) = log(4 + 7) which becomes log(11) = log(11) which confirms the solution is good.
b.)
e^(x^2-3) = e^(2x)
this is true if and only if x^2 - 3 = 2x
subtract 2x from both sides to get x^2 - 2x - 3 = 0
factor to get (x-3) * (x+1) = 0
solve for x to get x = -1 or x = 3.
when x = -1, e^(x^2-3) = e^(2x) becomes e^(1-3) = e^(2*-1) which becomes e^(-2) = e^(-2) which confirms the solution is good.
when x = 3, e^(x^2-3) = e^(2x) becomes e^(9-3) = e^(2*3) which becomes e^(6) = e^(6) which confirms the solution is good.
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