Question

log base 4 of ( 2 log base 3 ( 1 + log base 2 ( 1 + 3 log base 3 of x) = 1/2

Answer 1

Answer:

Answer is in attached pic.

Answer is 3

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Answer 2

Hence x = 3.

Explanation:

log₄ (2log₃ (1+log₂ ( 1+ 3log₃ x)  = 1/2

using logarithm property:

log base b (a) = k

=> a = b^k

Thus,

2 log₃ (1 + log₂ (1 + 3log₃ x)) = 4

log ₃ (1 + log₂ (1 + 3log₃ x ) = 1

1 + log₂ ( 1 + 3logx) = 3¹

log₂ (1 + 3log₃ x) = 2

1 + 3log₃x = 2²

3log₃x = 4 - 1

3log₃x  = 3

log₃ x = 1

x = 3.

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