Logarithm Problem

Question

Given the formulas 2^x+2^y=10 and x+y=4, what are the values of x and y?

Answer 1

Try substitution, where y=4-x.

2^x+2^4-x=10

2^x+2⁴2^-x=10

2^x+16/2^x=10

2^2x+16=10(2^x) (multiply every term by 2^x)

(2^x)²-10(2^x)+16=0

Let u = 2^x

u²-10u+16=0

Factor and solve for u (getting values of 8 and 2).

2^x=8 or 2^x=2

Solve for x and for each value of x find the corresponding value for y.

Answer 2