Question

a^log b-log c×b^log c-log a ×c^loga-log b has a value of​

Answer 1

$\huge\underline\bold \green{ QUESTION }: \\ </p><p>$

$\bold{ {a}^{ log(b) - log(c) } } {b}^{ log(c) - log(a) } {c}^{ log(a) - log(b)}$

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$\huge \underline \bold \red{solution}:$

$= > \frac{ {a}^{log(b) } }{ {a}^{ log(c) } } \times \frac{ {b}^{ log(c) } }{ {b}^{ log(a) } } \times \frac{ {c}^{ log(a) } }{ {c}^{ log(b) } } \\ = > \frac{{a}^{log(b) }{b}^{ log(c)} {c}^{ log(a) }}{{a}^{ log(c) }{b}^{ log(a) } {c}^{ log(b) }} \\ = > \frac{ ( {b}^{ log(a) }) \times ( {c}^{ log(b) }) \times ( {a}^{ log(c) } ) }{{a}^{ log(c) }{b}^{ log(a) } {c}^{ log(b) }} \\ = > 1$

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$\underline \bold \blue{formulas \: used}:$

$= > {a}^{m - n} = \frac{ {a}^{m} }{ {a}^{n} } \\ = > {a}^{ log_{e}(b) } = {b}^{ log_{e}(a) }$

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$\underline \bold \red{final \: answer}:$

$\huge\bold{1}$

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$\underline\bold{hope \: it \: helps \: you}$