Question

$<b><big>Hello Friends !!!$

$<b><big>Answer the above question$


$<b><big>Chapter : Logarithm$

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Answer 1

Given Equation : 2ˡᵒᵍ₃⁷ - 7ˡᵒᵍ₃²



Let 2ˡᵒᵍ₃⁷ = x and 7ˡᵒᵍ₃² = y

∴ Given equation : x - y



Now,
2ˡᵒᵍ₃⁷ = x


taking log on both sides,


log₃2ˡᵒᵍ₃⁷ = log₃x

log₃7 x log₃2 = log₃x

∴ 3ˡᵒᵍ₃⁷ ˣ ˡᵒᵍ₃² = x ....( i )



Also, 7ˡᵒᵍ₃² = y


taking log on both sides


log₃7ˡᵒᵍ₃² = log₃y

log₃2 x log₃7 = log₃y

∴ 3ˡᵒᵍ₃² ˣ ˡᵒᵍ₃⁷ = y


As log₃2 x log₃7 = log₃7 x log₃2, 3ˡᵒᵍ₃² ˣ ˡᵒᵍ₃⁷ is also equal to 3ˡᵒᵍ₃⁷ ˣ ˡᵒᵍ₃².


∴3ˡᵒᵍ₃⁷ ˣ ˡᵒᵍ₃² = y ....( ii )



∴ x - y

Substituting the values of x and y from ( i ) and ( ii )

3ˡᵒᵍ₃⁷ ˣ ˡᵒᵍ₃² - 3ˡᵒᵍ₃⁷ ˣ ˡᵒᵍ₃²

0



Therefore the value of 2ˡᵒᵍ₃⁷ - 7ˡᵒᵍ₃² is 0.

$\:$

Answer 2

$\huge \bold {\mathfrak {Hello \: BigBang!!}}$

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@youranswer in attachment

$= > \: therefore \: the \: value \: of \\ {2}^{ log_{3}(7) } - {7}^{ log_{3}(2) } \: is \: 0.$
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Hope it will help you

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