Question

Rewrite the expressions as a single logarithm. log. x-3 -2 log.y-3log. x+1

Answer 1

by properties on logarithm we have

1) m*log(a) = log (a^m) .

2) log(a) +log(b)= log(ab)

3) $\large log(a)-log(b)=log\left ( \frac{a}{b} \right )$

by applying first property ,to second and third term the expression becomes

$\large log_4(x-3)-log_4(y^2)-log_4(x+1)^3$

now apply 3rd property to first two expression becomes

$\large log_4(\frac{x-3}{y^2})-log_4(x+1)^3$

then apply third property again . it becomes

$\large log_4\left (\frac{x-3}{y^2(x+1)^3} \right )$

so this is answer