Question

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Answer 1

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Answer 2

GIVEN :–

$\\ \implies \sf x - log(48) + 3 log(2) = \dfrac{1}{3} log(125) - log(3)$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \implies \sf x - log(48) + 3 log(2) = \dfrac{1}{3} log(125) - log(3)$

• We should write this as –

$\\ \implies \sf x - log(48) + 3 log(2) = \dfrac{1}{3} log( {5}^{3} ) - log(3)$

• Using property –

$\\ \implies \sf log( {a}^{b} ) = b. log(a)$

$\\ \implies \sf x - log(48) + 3 log(2) = \dfrac{3}{3} log(5) - log(3)$

$\\ \implies \sf x - log(48) + 3 log(2) =log(5) - log(3)$

$\\ \implies \sf x - log( {2}^{4} \times 3) + 3 log(2) =log(5) - log(3)$

• Using identity –

$\\ \implies \sf log(m.n) = log(m) + log(n)$

$\\ \implies \sf x - \{log( {2}^{4} ) + log(3) \} + 3 log(2) =log(5) - log(3)$

$\\ \implies \sf x - log( {2}^{4} ) - log(3)+ 3 log(2) =log(5) - log(3)$

$\\ \implies \sf x - 4log(2) - log(3)+ 3 log(2) =log(5) - log(3)$

$\\ \implies \sf x - log(2) - log(3)=log(5) - log(3)$

$\\ \implies \sf x - log(2)=log(5)$

$\\ \implies \sf x=log(5) + log(2)$

$\\ \implies \sf x=log(5 \times 2)$

$\\ \implies \large{ \boxed{ \sf x=log(10) }}$