Question

Correct answer with appropriate explanation will go for the brainliest!!

Question:
Prove that the base of logarithm cannot be negative.

#100th question

Answer 1

Answer:

Base of logarithm and power functions are not so different infact

$log_{b}(a) = x \implies \: a = {b}^{x}$ .

Answer 2

STEP-BY-STEP EXPLANATION:

.

To Proof ; The base of logarithm cannot be negative.

$\sf The \: base \: of \: Logarithm:$

$\bf log_{b}(a) = x \implies a = {b}^{x}$

To Proof that, The base of logarithm cannot be negative.

We need to see the logarithm within negative base.

$\sf Let's,$

• $\sf x = \frac{1}{2}$

$\sf And,$

• $\sf b < 0$

$\sf So,$

$\sf b \: will \: be \: a \: negative \: number.$

$\sf Here \: we \: found \: that,$

$\sf \implies a = {b}^{x}$

$\sf \implies a = {(Negative \: Number)}^{ \frac{1}{2} }$

$\sf \implies a = \sqrt{{Negative \: Number}}$

$\sf So,$

$\sf If \: we \: make \: the \: base \: of \: logarithm \: negative.$

$\sf We \: will \: find \: A \: imaginary \: value \: of \: a.$

$\sf Therefore,$

• $\sf The \: base \: of \: logarithm \: cannot \: be \: negative.$

Hence Proved,