Question

(a) Solve the following equations for x where possible, giving your solutions correct to three decimal places.

(i) 3^x+1 -1=5

(ii) 3×4^x =4×4^1-2x

(b) Confirm that any solutions you found in part (a) are (approximately) correct by sub-situiting into the original equation.

Answer 1

(i) assuming the usual sloppiness with parentheses,

3^(x+1) - 1 = 5
3*3^x = 6
3^x = 2
x = log_₃2

(ii)
3*4^x = 4*4^(1-2x)
3*4^x = 4^2 /4^(2x)
3*4^(3x) = 16
4^(3x) = (16/3)
3x = log_₄(16/3)
x = (1/3) log_₄(16/3)