Prove the following exponential identity prove the

Question

1. Prove the following exponential identity

3 (9^x+2) = 3^2x+5

2. Prove the following exponential identity

16^x-2y = 2^4x/4^4y

3. Prove the following logarithmic identity

log_1/2log₂ (21og₂ 4) = - 1

4. Prove the following logarithmic identity

log₂ x/y + 4log₂ 4 √(y/x) = 0

5. Solve the exponential equation

8^x+1 · 4^{x- 2} =16^x

6. Solve the exponential equation for x and for y

3^x+1 · 2^y-2 = 36

7. Solve the logarithmic equation

log₂ log₂ 4^x-2 = 1

8. Solve the exponential inequality.

27(3^2x+1) > 3^x+5 + 3³

9. Solve logarithmic inequality.

3log x < 2log (1/x) + 1