Question

Lim x-->0 [ln(sinx)-lnx]

Answer 1

`\bf \lim\limits_(x\to 0)\ ln[sin(x)]-ln(x)\\\\ -----------------------------\\\\ log_{{ a}}\left( (x)/(y)\right)\implies log_{{ a}}(x)-log_{{ a}}(y)\qquad thus\\\\ -----------------------------\\\\ ln[sin(x)]-ln(x)\implies ln\left[ \cfrac{sin(x)}{x} \right]\implies ln(1)\implies 0`