Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

1

You have to make a list of x and y values.

1) For your first equation (y = 4^{3x}) you will have

x 0 1/3 1/2 1

y 1 4 8 64

Since 4^{3x} = 8 your anwerr is x = 1/2. For the right side y = 8 - horizontal line intersecting y=4^{3x}

at x = 1/2.

2) The same way, for the second equation you can make a chart

x 0 1/4 1/2 1

y 1 2 4 16

Since the right side is y =7, function y = 4^{2x} will intersect y = 7 line at 1/2 < x <1. If you solve it analytivally (by taking logarithms) you will find that in this case x = 0.702 (x = ln7/2ln4). Use the numbers shown to sketch the graph to make sure that x = 0.702. Good luck!