Question

Solve
log 3x -log 13=2. Round to the nearest thousandth if necessary.

Answer 1

`\bf \textit{Logarithm of rationals}\\\\ log_a\left( (x)/(y)\right)\implies log_a(x)-log_a(y) \\\\\\ \textit{Logarithm Cancellation Rules}\\\\ log_a a^x= x\qquad \qquad \boxed{a^(log_ax)=x}\\\\ -------------------------------\\\\ log(3x)-log(13)=2\implies log_(10)(3x)-log_(10)(13)=2 \\\\\\ log_(10)\left( (3x)/(13) \right)=2\implies 10^{log_(10)\left( (3x)/(13) \right)}=10^2\implies \cfrac{3x}{13}=2 \\\\\\ 3x=26\implies x=\cfrac{26}{3}\implies x=8(2)/(3)`