Download MAC 1140 Strategy for Solving Exponential Equations 1) Isolate the

MAC 1140
Strategy for Solving Exponential Equations
1) Isolate the exponential term.
2) Try to get the bases the same on both sides of the equation and set the powers
equal to each other.
3) If you can’t get the bases equal to each other, you must use logarithms.
Either:
a) Take the log of both sides and solve for x by using the power rule for logs.
or b) Change to log form and solve for x. (You might have to use the change of
base formula if you do it this way.)
4) The above procedures will work most of the time but there are some exponential
equations that will require other methods. For example:
(An exponential equation of quadratic form):
Solve: 2e2 x  7e x  15  0
(2e x  3) (e x  5)  0
2e x  3  0 or
ex  5  0
3
or
ex 
e x  5 (this equation has no solution)
2
 3
x  ln    .4055
 2
Strategy for Solving Logarithmic Equations
1) Rewrite the equation by combining logarithms so that it is in one of the following two
log a (bx  c)  log a (dx  e)
forms:
log a x  b or
2) If the log equation is of the form log a x  b , change to exponential form and solve.
3) If the log equation is of the other form, use the one-to-one property of logarithms,
set the arguments equal to each other and solve.
4) These procedures will work most of the time, but there are some log equations that
will require other methods. For example:
(A log equation of quadratic form):
Solve: (log 2 x)2  3 log 2 x  10
(log 2 x)2  3 log 2 x  10  0
(log 2 x  5) (log 2 x  2)  0
log2 x  5
or
log 2 x  2
2 x
x  32
or
or
2 2  x
x = 1/4
5
*Remember to check your answer: A logarithm, log a x , must have a > 0, a  1 , and x > 0.