Mathematical logical Solution:

log [1/(10^10)] = -10 log(10) = -10 ->A

log [1/(10^20)] = -20 log(10) = -20 ->B

Now,

So, LHS: A + 3B + 80 + 90

=> -10 + 3(-20) + 80 + 90

=> 100 -> RHS

Hence proved! ( No negative numbers though)

Hence, A is log[1/(10^10)] and B is log[1/(10^20)]

Explanation
Equation 1: 5 + 10 + 10 = 25  (So the value of a PLANT with 5 leaves is 5; Also note that there are two plants one beneath the other in second and third part of the equation 1.

Equation 2: 8 + 8 + 8 = 24  (If you look closely, you can see the number 3 on top of each Tortoises. So the value of a TORTOISE = 5)

Equation 3: 2 x 2 x 2 = 8   (So the value of a CATERPILLAR = 2)

Equation 4: 3 + 3 + (-3) = 3   (Since on bug is moving backwards its value is negative. So the value of one BUG = 3)

Equation 5: (5 + 3) + (4 + 2 + 2) x (3 + 3)

 (Here in the first part of equation there is a bug on the face of the Tortoise and the Tortoise has no number 3 on its body)
(In the second part of this equation, there are only 4 leaves for the plant and you can see two Caterpillars in the plant pot)

(In the third part of this equation, there are two bugs, one beneath the other)

=> 8 + 8 x 6

=> 8 + 48

=> 56

Final Answer = 56