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secondary 3 | A Maths
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Please help as soon as possible. Thanksss (Answer: a. Yes b. No)
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The domain of log cannot be negative nor zero
Range of log is real number
A^x = Y
For all x, Y is positive
If x is positive but not zero, -x is negative
1/A^x = A^(-x) = 1/Y and A is positive,
For X is real, as any number
X = Log(baseA)Y, at here we define C is positive
For negative X
-X = - log(baseA)Y = log(base A)(1/Y)
As 1/Y is positive, therefore for all X the corresponded Y is all positive, except when X = 0
When X= 0, for the continuity of function
Y = 1/Y => Y ^2 = 1 => as Y >0, Y =1
Therefore when X =0, Y =1,
And alll “Y” is positive for A is positive, if A is negative, X is only valid when it is multiple of 0.5 and Y cannot real or imaginary