Section 3.4
Exponential and Logarithmic
Equations
Exponential Equations
Example
Solve for x: 643 x  322 x
Example
Solve for x: 3x  21
Example
Solve for x: 3x  2  73 x 1
Logarithmic Equations
Logarithmic expressions are defined only for logarithms of
positive real numbers. Always check proposed solutions of
a logarithmic equation in the original equation. Exclude from
the solution set any proposed solution that produces the logarithm
of a negative number or the logarithm of 0.
Example
Solve for x: log 2 ( x  5)  4
Example
Solve for x: 4 ln(3 x)  12
Example
Solve for x: ln(1)  ln(3 x  2)  ln( x)
Example
Solve for x: 3logx   log 27
Example
Solve for x: log( x  3)  log( x  3)  log x
Applications
Visualizing the Relationship Between Blood Alcohol Concentration and the
Risk of a Car Accident
Medical research indicates that the risk of having a car
accident increases exponentially as the concentration of
alcohol in the blood increases. The risk is modeled by
R=6e12.77 x
where x is the blood alcohol concentration and R, given
as a percent, is the risk of having a car accident. What
blood alcohol level corresponds to an 80% chance of an
automobile accident?
Example
nt
 r
Formula for Compound Interest A=P 1  
 n
How long will it take $3,000 to grow to $30,000 at
5% annual interest compounded semi-annually.
Solve for x: ln(x+3)=6
(a) e 6
(b) e 6  3
(c) e3
(d) e3  6
Solve for x: 7
(a)
(b)
(c)
(d)
4 ln 3
2 ln 7
ln 7  ln 3
2 ln 7
ln 7
4 ln 3
4 ln 3  ln 7
2 ln 7
2 x1
3
4