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secondary 3 | A Maths
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Koyuki Sky
Koyuki Sky

secondary 3 chevron_right A Maths chevron_right Singapore

Please help as soon as possible. Thanksss (Answer: a. Yes b. No)

Date Posted: 3 years ago
Views: 164
Eric Nicholas K
Eric Nicholas K
3 years ago
When you are taking a logarithm, you are finding the power of an expression. Recall that loga b = c is an alternative form of the expression a^c = b. As we know it too well, we can have negative powers as learnt in indices. For example, 2^-2 = 1/4. In logarithm form, the negative power will appear on the right hand side. So yes, a logarithm can have a negative value.

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In real number

The domain of log cannot be negative nor zero

Range of log is real number
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Kahwai
Kahwai's answer
232 answers (A Helpful Person)
1st
How to justify

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
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Kahwai
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232 answers (A Helpful Person)