Question

expand the following log a^x ×b^y/c^x​

Answer 1

We are given

$\longrightarrow \sf {log \Bigg\lgroup \dfrac{{a}^{x} * {b}^{y}}{{c}^{x}} \Bigg\rgroup}$

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.