Find the value of loge 144.

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Question

Find the value of

{log}_{e}

144.

Options:

A . 2loge12

B . 4loge2 + 2loge3

C . 3loge2 + loge18

D . All of these

Answer: Option D
:
D

{log}_{e}

144 =

{log}_{e} 12^{2}

=

2 {log}_{e} 12

(option A)
Factors of 144 =

2^{4}

\times

3^{2}

{log}_{e}

144 =

{log}_{e}

(

2^{4}

\times

3^{2}

)
=

{log}_{e} 2^{4}

+

{log}_{e} 3^{2}

=

4 {log}_{e} 2

+

2 {log}_{e} 3

(option B)

{log}_{e}

144 =

{log}_{e}

(

2^{3}

\times

18) =

{log}_{e} (2^{3})

+

log 18

=

3 {log}_{e} 2

+

log 18

(option C)

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