find the value of log 324 to the base of 3root2
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Answered by
0
Answer:
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Answered by
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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