Solve giving your answer to 3 significant fiqures

Question

1. 3^z - 4 = 0
2. 6^x - 4(2^x) - 3^x + 4= 0
3. The curve with equation y= 5(3^2x) - 6(3^x) intersects the curve with equation y=5(3^x) - 2 at two points.

 We have to find the coordinates of each of these two points.

Answer 1

1. 3^z = 4 => z log 3 = log 4 and z = (log 4)/log 3

 

2. 3^x2^x - 4(2^x) - 3^x + 4 = 0 factors as 3^x(2^x - ) - 4(2^x - 1) = 0 => (3^x - 4)(2^x -1) = 0

    2^x - 1 = 0 => x = 0

    3^x - 4 = 0 has the same solution as part 1.

 

I will leave looking up the logarithms and the division to you.