Using Logarithms to Solve Exponential Equations

Rules for Logarithms
If A and B are positive real numbers and p is any real number, then
1. log (A • B) = log A + log B
2. log (A/B) = log A - log B
3. log A^p = p log A
4. log 1 = 0

Use the function f(t)=100(0.976)^t to determine how long it will take for 100 milligrams of strontium-90 to decay to 10 milligrams. Round the answer to the nearest integer.

t=?years

100(0.976)^t = 10

=> (0.976)^t = 0.1

=> t log(0.976) = log 0.1

=> t = log 0.1 / log(0.976) = 95 years

10 = 100(.976^t)
.1 = .976^t
log .1 = t * log.976t
t = (log .1)/log 94.8 = 95 years

10=100(0.976)^t
.1=(0.976)^t
ln(.1)=tln(.976)
t=ln(0.1)/ln(.976)

10=100(0.976)^t
10/100=(0.976)^t
log(.1)=log(0.976)^t
log(.1)=t*log(0.976)
t=log(.1)/log(0.976)