Exponential Equation Prob

Question

$$4^x + 4^y = 10$$ $$4^x - 4^y = 8$$ $$2^x . 2^y = ?$$ I couldn't understand this problem, also i couldn't solve the problems which like this. So I want to learn how to solve this problems are. Thanks for helping!

Answer 1

Try adding and subtracting the equations.

Adding we get $2\times4^x=18\implies4^x=3^2\implies2^{2x}=3^2\implies (2^x)^2=3^2$.Taking square root $2^x=3$

Subtracting we get,$2\times4^y=2\implies 4^y=4^0\implies y=0$.So,$2^y=2^0=1$

So,now, just plug in the values of $x$ and $y$ into $2^x\cdot2^y=3\cdot1=3 $

Answer 2

Hint:

First add the two equations to help find $x$.

Then subtract the two equations to help find $y$.