Question

if log (a square ×b cube)- log(a cube÷a square)​

Answer 1

Step-by-step explanation:

log(a²*b³)-log(a³/a²)

=log(a²*b³)-log a

=log(a²*b³/a)

=log(a*b³)

=log a+log b³

=log a+3log b

Answer 2

$\rm \underline{ \red{\large{ question}}}$

$: \implies\rm log( {a}^{2} \times {b}^{3} ) - log( {a}^{3} \div a {}^{2} )$

$\rm \underline{ \red{\large{ solution}}}$

$: \implies\rm log( {a}^{2} \times {b}^{3} ) - log( {a}^{3} \div a {}^{2} )$

$\rm : \implies \: log( { a}^{2} {b}^{3} ) - log( \dfrac{ {a}^{3} }{ {a}^{2} } )$

$\rm : \implies \: log( { a}^{2} {b}^{3} ) - log( { {a}^{} }{ {}^{} } )$

Using this property

$\boxed{\rm \: log( \dfrac{x}{y} ) = log(x) - log(y) }$

We get

$\rm : \implies \: log( { a}^{2} {b}^{3} ) - log( { {a}^{} }{ {}^{} } )$

$: \implies \rm \: log( \dfrac{ {a}^{2} b {}^{3} }{a} )$

$\rm : \implies log(a {b}^{3} )$

$\rm \underline{ \red{\large{ answer}}}$

$\rm : \implies \boxed{ \rm log(a {b}^{3} ) }$