Math, asked by tshanker709, 11 months ago

find the value of log 324 to the base of 3root2​

Answers

Answered by shivam1459
0

Answer:

mmmm..................

Answered by skvijay36
0

Answer:

The value of\log_{(3\sqrt{2})}324log

(3

2

)

324 is "4".

Step-by-step explanation:

Let x =\log_{(3\sqrt{2})}324log

(3

2

)

324 ..... (1)

To find, the value of \log_{(3\sqrt{2})}324log

(3

2

)

324 = ?

∴ 324 = 2 × 2 × 3 × 3 × 3 × 3

=2^{2} \times 3^{4}=2

2

×3

4

=\sqrt{2}^{4} \times 3^{4}=

2

4

×3

4

=(3\sqrt{2})^{4}=(3

2

)

4

Now, equation (1) becomes

x = \log_{(3\sqrt{2})}(3\sqrt{2})^{4}x=log

(3

2

)

(3

2

)

4

x =4 \log_{(3\sqrt{2})}(3\sqrt{2})x=4log

(3

2

)

(3

2

)

= 4

[ ∵ \log_aalog

a

a = 1 ]

Hence, the value of\log_{(3\sqrt{2})}324log

(3

2

)

324 is "4"

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