Need some Algebra 2 help?

Question

I need help with a couple problems:

ln e^ln x - ln(x-3) = ln 2

2^x+3=5^x

2e^5x+2=8

10^log 8 (base 10)

and this system of equations:

9x^2+4y^2=36

x^2+9y^2=9

My problem is that I need exact answers. Can you help? Thanks

Answer 1

9x^2+4y^2=36

x^2+9y^2=9

eqn2 times 9 minus eqn 1 gives

77 y^2 = 45  or y^2 = 45/77 or y = (+/-) sqrt(45/77)

x^2 = 9 - 9 * (45/77) = 288/77 or x = (+/-) sqrt(288/77)