Question

Write the expression as a single logarithm

Answer 1

We have to use the following log rules here

$a log (b) = log b^a , log(a) + log(b) = log(ab), log (a)-log(b) = log(a/b)$

So for the given question , that is

$18log \sqrt x +9 log \sqrt [3]{x}-log 10 = log(x^{18/2}) + log(x^{9/3})-log 10$

$log(x^9)+log(x^3)-log 10= log(x^9*x^3)-log 10$

$=log(x^{12}) - log 10 = log(\frac{x^{12}}{10})$