Expand the following log a^x ×b^y/c^x

1.	Expand the following log a^x ×b^y/c^x
Answer» re given $\longrightarrow \sf {log \Bigg\lgroup \dfrac{{a}^{<klux>X</klux>} * {b}^{y}}{{c}^{x}} \Bigg\rgroup}$ We can write it as, $\longrightarrow \sf { log {a}^{x} + log{b}^{y} - log{c}^{x}}$ $\longrightarrow \sf{ xloga + y logb - xlogc}$ Hence, your required answer is, $\longrightarrow \underline{\underline{\sf{ xloga + y logb - xlogc}}}$ $\sf{\\ \\}$ FORMULAS Used:- $\quad \quad \bullet \sf{log (\dfrac{m}{n}) = logm - logn}$ $\quad \quad \bullet \sf{log (mn) = logm + logn}$ $\quad \quad \bullet \sf{log {m}^{n} = nlogm}$ $\sf{\\ \\}$ $\longrightarrow \sf{ xloga + y logb - xlogc}$ can be SIMPLIFIED, $\longrightarrow \sf{ x(loga - logc) + ylob}$ , but since the question is asking for expanding the EXPRESSION, it is better not to take x as common.

Answer»

re given

$\longrightarrow \sf {log \Bigg\lgroup \dfrac{{a}^{<klux>X</klux>} * {b}^{y}}{{c}^{x}} \Bigg\rgroup}$