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1. Expand the following:
2. Condense the following:
4log316log1log2
1 22 xxx
Warm-up
14
5log
2
2 x
x
How tall and wide is the arch if its curve is described by the exponential equation below
27672.688597.693
0100333.00100333.0 xx eey
Summary
1. Log = number or Exponential form = number
2. Exponent = Exponent (same base)
3. Exponent = Exponent (different base)
4. log = log
uabu ba )(log
vuaa v u
vuvu baba loglog
vuvu aa )(log)(log
Log and Exponential Equations can be solved using various approaches
Choose an appropriate method and solve for x:
644 1) 2 x
538 2) 2 x
)1(log)6(loglog 3) 333 xx Hint: Use log properties and rewrite the left side as a single log expression.
4.6 Logarithmic and Exponential Equations
1. Express the left side as a single logarithm.
2. Rewrite as an exponential expression
Always check your solution to assure the solution is in the domain of the problem.
)(log23)23(log 22 xx
24 4Solve log 9 log 3 3 0x x
Solving a Logarithmic Equation
Solve an Exponential Equation with a different base on each side.
Take the natural log (base e) or
log (base 10) of each side
Solve an Exponential Equation that is quadratic in form
Summary
1. Log = number or Exponential form = number
2. Exponent = Exponent (same base)
3. Exponent = Exponent (different base)
4. log = log
uabu ba )(log
vuaa v u
vuvu baba loglog
vuvu aa )(log)(log
This is an APPROXIMATE solution.
Solve using your graphing calculator