Question

Find x if x -48 + 3 log 2'= 1/3 log 125' - log 3 ​

Answer 1

${ \bf{ \underline{ \blue{ \underline{ \blue{ Given}}}} : - }}$

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

${ \bf{ \underline{ \blue{ \underline{ \blue{ To-Find}}}} : - }}$

• Value of x

Property and Identity to be used :-

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

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

${ \bf{ \underline{ \blue{ \underline{ \blue{ Solution }}}} : - }}$

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

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

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

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

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

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

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

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

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

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

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

$\\ \implies \sf x=log(10)$

$\\ \implies \sf x= 1$

$\small{\underline{\sf{\blue{Hence-}}}}$

Value of x is = 1

Answer 2

${ \bf{ \underline{ \green{ \underline{ \green{ Given}}}} : - }}$

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

${ \bf{ \underline{ \green{ \underline{ \green{ To-Find}}}} : - }}$

• Value of x

Property and Identity to be used :-

$↦ \sf log( {a}^{b} ) = b. log(a)$

$↦ \sf log(m.n) = log(m) + log(n)$

${ \bf{ \underline{ \green{ \underline{ \green{ Solution }}}} : - }}$

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

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

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

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

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

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

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

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

$↦\sf x - log(2)=log(5)$

$↦ \sf x=log(5) + log(2)$

$↦ \sf x=log(5 \times 2)$

$↦ \sf x=log(10)$

$↦ \sf x= 1$