Question

y - 1
(i) If log x + log y = log (x + y), then x =
(ii) If 2 log a + 3 log 6 - 2 = 0, then a²b3 = 100​

Answer 1

${\red {{\bold{ \huge \dag }}\bold {\huge{{\mathcal {\underline{Answer}}}} \dag}}}$

$\star \: \underline \blue{solution} \blue{ : }$

QUESTION NO 1.

$\bold{ log(x) + log(y) = log(x + y) }$

$\longrightarrow \: log(xy) = log(x + y)$

$\longrightarrow \: xy = x + y$

$\longrightarrow \: x(y - 1) = y$

$\longrightarrow {\boxed {\mathfrak { x = \frac{y}{y - 1} }}}$

QUESTION NO 2.

$\bold {\boxed{I \: guess \: your \: question \: is \: 2 \: log(a) + 3 \: log(b) - 2 = 0}}$

$\star \: \: \underline \blue{given} \blue{ : }$

$2 \: log(a) + 3 \: log(b) - 2 = 0$

$\star \: \: \underline \blue{prove} \blue{ : }$

${a}^{2} {b}^{3} = 100$

$\star \: \: \underline \blue{solution} \blue{ : }$

$\bold{2 \: log(a) + 3 \: log(b) - 2 = 0}$

$\longrightarrow \: log( {a}^{2} ) + log( {b}^{3} ) = 2$

$\longrightarrow \: log( {a}^{2} {b}^{3} ) = 2 log(10)$

$\longrightarrow \: log( {a}^{2} {b}^{3} ) = log( {10}^{2} )$

$\longrightarrow \: \bold{\boxed {\mathfrak{{a}^{2} {b}^{3} = 100}}}$ Proved