15(1+0.6/4)^4t = 30e^-0.25t, solve for t

x =

                ≈ 0.856

Step-by-step explanation:

 15(1 + )⁴ˣ = 30e⁻°²⁵ˣ

 15(1.15)⁴ˣ = 30e⁻°²⁵ˣ

÷30           ÷30          

0.5(1.15)⁴ˣ = e⁻°²⁵ˣ

ln[0.5(1.15)⁴ˣ] = ln[e⁻°²⁵ˣ]

ln 0.5 + ln(1.15)⁴ˣ = -0.25x

ln + 4x ln(1.15) = -0.25x

4x ln(1.15) + 0.25x = -ln

x(4 ln(1.15) + 0.25) = -ln 0.5

x =

  ≈ 0.856

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752