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5 Responses to “Solving exponential equations by taking the natural log of both sides? Please help?”

1. Clara Z Says:
   January 15th, 2008 at 11:27 pm

   a)M(0) = 6e ^0.18 x0 = 6e^0 = 6*1 =6

   b)M(t) = 6e ^ 1.18t = 90
   e^1.18t = 90/6
   1.18t = ln(90/6)
   t = (ln(90/6))/1.18

2. Elaine K Says:
   January 17th, 2008 at 12:01 pm

   a). at t = 0;

   M(0) = 6e ^1.18 *0 = 6e^0 = 6

   (recall that any number to the power of zero is one).

   b) for M(t) = 90;

   6e ^ 1.18t = 90

   e ^ 1.18t = 15

   Take natural log on both sides;

   1.18t = ln (15)

   t = ln (15) / 1.18

   And your problem is solved!

3. maSC Says:
   January 19th, 2008 at 1:23 am

   You answered correctly for (a) with wrong solution.
   Answer for a):
   M(0) = 6e ^1.18 x0
   = 6e^0
   =6

   (b)
   M(t) = 6e ^ 1.18t
   90=6e^1.18t
   15=e^1.18t

   Note that ln is the natural logarithm meaning log base e

   ln15=ln(e)^1.18t
   ln15=1.18t ln(e)
   ln15=1.18t
   (ln15)/1.18=t
   t = (ln15)/1.18
   That’s the answer but you’ll be needing the calculator to get the exact value.

4. Amine Says:
   January 21st, 2008 at 11:15 pm

   man!! e^(1.18*0) = e^0 = 1 this is why M(0) = 6 for a)

   b)

   M(t) is the mice’s population, therefore if the population is 90, M(t) = 90

   So, 90 = 6e^(1.18t)
   e^(1.18t) = 15

   since, 15 is a constant function, it is continuous on R (real numbers); and e^(1.18t) is defined on R and by definition continuous on it,
   we can put the LN (natural log) in both side of the equality,

   ln(e^(1.18t)) = ln(15)
   hence, 1.18t = ln(15) {because, ln is the inverse function of e, in other words (e o ln)(x) = (ln o e)(x) = x }

   then, 1.18t = 2.71 (approximately)

   Finally, t = 2.29
   Basically, in a bit more than two months there will be 90 mice

   if u wanna make it more accurate (but i guess there is no real need)
   1 month –> 30 days
   0.29 month –> ?
   ?=0.29*30 = 8.7

   so in 2 months and about 9 days there will be 90 mice……

5. como Says:
   January 24th, 2008 at 7:43 pm

   Part a)
   M = 6 e^0
   M = 6

   Part b)
   90 = 6 e^(1.18 t )
   15 = e^(1.18 t )
   ln 15 = 1.18 t ln e
   ln 15 = 1.18 t
   t = ln 15 / 1.18
   t = 2.29 months