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natta225 [31]
3 years ago
15

Evaluate the logarithm. ln=1/√e^3

Mathematics
2 answers:
Alenkinab [10]3 years ago
7 0

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}

Lyrx [107]3 years ago
4 0

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

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