Question

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Correct answer with appropriate explanation will go for the brainliest!! Question: Prove that the base of logarithm cannot be negative.
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Answer 1

$\bold { \red{EXPLANATION: }}$

WHAT IS LOGARITHM:

Logarithm, the exponent or power to which a base must be raised to yield a given number.

Expressed mathematically, x is the logarithm of n to the base b if

${b}^{x} = n, in \: which \: case \: one \: writes \: x = log_{b}n$

For example,

${2}^{3} = 8;therefore, 3 \: is \: the \: logarithm \: of \: 8 \: to \: base \: 2, or \: 3 \\ = log_{2}8$

WHAT HAPPENS WHEN THE BASE IS NEGATIVE ?

If b < 0, this can pose some problems if e.g. y is not a positive integer.

For example,

If b = -4 and y = 1/2, then b^y = x is equal to the square root of -4.

This wouldn't give any real solutions!

Therefore,

THE BASE OF LOGARITHM CANNOT BE NEGATIVE.