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