Question

Evaluate the logarithm. ln=1/√e^3

Answer 1

Answer:

option b

-3/2

Step-by-step explanation:

Given in the question an expression

ln$\frac{1}{\sqrt{e^3} }$

First apply logarithm divide rule

$ln\frac{1}{\sqrt{e^3} }$ = ln1 - ln√e³

ln(1) = 0

so

ln1 - ln√e³ = 0 - ln√e³

-ln√e³ = -ln(e³)^1/2

Apply logarithm power rule

- ln(e³)^1/2 = -lne$^\frac{3}{2}$

-3/2ln(e)

As we know that

ln(e) = 1

so,

-3/2(1)

-3/2

Answer 2

Answer:

b. $-\frac{3}{2}$

Step-by-step explanation:

The given logarithm is

$\ln(\frac{1}{\sqrt{e^3} } )$

Use the quotient rule of logarithm; $\ln(\frac{a}{b})=\ln(a)-\ln(b)$

$=\ln(1)-\ln(\sqrt{e^3})$

$=\ln(1)-\ln(e^{\frac{3}{2}})$

Use the power rule; $\ln(a^n)=n\ln(a)$

$=\ln(1)-\frac{3}{2}\ln(e)$

Recall that logarithm of 1 is zero and also logarithm of the base is 1.

$=0-\frac{3}{2}(1)$

$=-\frac{3}{2}$