Enhancement: Number System (Indices & Logarithms)

1.    Solve the equations:

(a)   e^2lnx = 9                                                        (b)    e^{x ln3} = 27

(c)  3e^-2x = 75                                                      (d)   e^2.5x = 40

  

2.   Solve these equations:

       (a)  2 log (x – 2) = log (2x – 5)              (b)  log (x² + 6) – log (x – 1) = 1

       (c)  log₂ (2x – 4) = 2 + log₂ (x²- 6)        (d)  log₃x – 2 log_x3 = 1

       (e)  9log_x 5 = log₅ x                              (f)   2 ln x = ln 3 + ln (6 – x)

       (g)   ln x = 2 + ln (1-x)                           (h)    e^ln(1-x) = 2x