Exponents and Logarithm

1. Find p in terms of q

   log₁₀[(¹⁄_2√2)(p+2q)] = ¹⁄₂[log₁₀p+log₁₀q]

2. Solve the simultaneous equations

   ln(^y/_x) = 2

   ln(x²/y³) = 7

3. Find x and y

   log_x+1y = 2

   log_y+1x = ¹/₄

4. Find x and y

   ln(^x/_y) = 1

   ln(x³/y²) = 5

5. Find x interms of ln 2

   ln 2^4x-1 = ln 8^x+5 + log₂16^1-2x

6. Solve

   (lnx)² - (ln2)(lnx) < 2(ln2)²

7. Solve for x

   log₂x - log₂5 = 2 + log₂3

8. Solve for x

   log₂(x+3) + log₂(x-3) = 4

9. Find a

   a = (log₂3)(log₃4)(log₄5)(log₅6)...............(log₃₁32)

10. Solve for x

    8^x-1 = 6^3x

11. Solve for x

    log₂(x-2) = log₄(x²-6x+12)

12. Solve for x

    x^lnx = e^(lnx)3

13. Solve for x

    2-log₃(x+7) = log_1/32x

14. Solve for x

    4^(x-1) = 2^x+8

15. Write as a single logarithm

    ln(x²-1) - 2ln(x+1) + ln(x² + x)