Question

The principle value of log(-5) is equal to​

Answer 1

Answer:

ai think your question is wrong

Answer 2

Answer:

The principal value of function log(-5) is $x=log(5)+i\cdot \pi}$.

Step-by-step explanation:

Recall the definition of the natural logarithm,

$a=e^{loga}$

The Euler's equation is,

$-1=e^{i\cdot \pi}$

Step 1 of 1

Consider the given logarithm function as follows:

log(-5)

Let $x$ = log(-5).

Taking exponential ($e$) on both the sides as follows:

⇒ $e^x=e^{log(-5)}$

Now, using the definition of log on the right-hand side.

⇒ $e^x=-5$ . . . . . (1)

Step 2 of 2

Rewrite the number $-5$ as follows:

⇒ $-5=5\cdot(-1)$

Substituting the values $e^x$ for $-5$, $e^{i\cdot \pi}$ for $-1$ and $e^{log5}$ for $5$ as follows:

⇒ $e^x=e^{log5} \cdot e^{i\cdot \pi}$

Simplify as follows:

⇒ $e^x=e^{log(5)+i\cdot \pi}$

Taking anti-㏒ on both the sides, we get

⇒ $x=log(5)+i\cdot \pi}$

Therefore, the principal value of the function log(-5) is $x=log(5)+i\cdot \pi}$.

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