Derivative of log(8)x+27log(9)x

1. Differentiate $x \log{\left(8 \right)} + x 27 \log{\left(9 \right)}$ term by term:

   1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x$ goes to $1$

      So, the result is: $\log{\left(8 \right)}$

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x$ goes to $1$

      So, the result is: $27 \log{\left(9 \right)}$

   The result is: $\log{\left(8 \right)} + 27 \log{\left(9 \right)}$

2. Now simplify:

   $$\log{\left(465197896024320477523121352 \right)}$$

The answer is:

$$\log{\left(465197896024320477523121352 \right)}$$