Logarithms

Question

Solve for x and y, the simultaneous equations 4^x+3 =32(2^x+y ) and 9^x + 3^y =1o

 

 

Ans: x=0.631 and y=1.631

 

 

 

Thank you :)

Answer 1

Solve for x and y (Ans: x=0.631 and y=1.631):
4^(x+3) = 32(2^(x+y)) Equation 1
9^x + 3^y = 10 Equation 2

4^(x+3) = 32(2^(x+y)) Equation 1
2^(2x+6) = 2^(x+y+5)
2x+6 = x+y+5
y = x + 1 Equation 3

9^x + 3^y = 10 Equation 2
3^(2x) + 3^(x + 1) = 10
(3^x)^2 + 3(3^x) - 10 = 0
(3^x+5)(3^x-2) = 0
3^x = -5 but exponential can’t be negative

3^x = 2

x log(3) = log(2)

x = log(2)/log(3) ~= 0.63092975357146

y = x + 1 ~= 1.63092975357146