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((x^(12))/(10))`