6-6: Solving Exponential Equations

Using logs to solve equations:

Solve the following equation for t to the nearest hundredth:

32 t x65 xe25

Using properties of logs:

The population of the US reached 250 million in 1990 and was growing at a rate of 1% per year. When, at this rate, would the population reach 300 million?

More applications:Carbon has a half-life of 5730 years. What is the approximate age of a skull found having 63% of its original concentration?

The Change of Base Theorem:Given bx=a

a) Definition of logs: b) Taking the log of both sides:

b

aab log

loglog

ax blog ab x loglog abx loglog

b

ax

log

log

Example:

Evaluate:

Try it with natural logs:

100log3