law of logarithms

Law of LogarithmsLaw of Logarithms

How do we write an exponential equation How do we write an exponential equation as a logarithmic equation?as a logarithmic equation?

Rewrite 3Rewrite 3² = 9 as a logarithmic ² = 9 as a logarithmic equation.equation.

loglog33 9 = 2 9 = 2 Write the following exponential Write the following exponential

equations as logarithmic equations.equations as logarithmic equations.

1)1) 8822 = 64 2) 10 = 64 2) 1000 = 1 = 1 3) 3 3) 3-2-2 = 1/9 = 1/9

Law of logsLaw of logsThey are similar to exponent They are similar to exponent

rules…rules…

1) B1) Bxx = Y = Y log logBB Y = X Y = X2) log2) logBB X = log X = logBB Y Y X = Y X = Y3) log3) logBB X + log X + logBB Y = log Y = logBB (XY) (XY)

andand

loglogBB X - log X - logBB Y = log Y = logBB (X/Y) (X/Y)4) Z4) Z● ● loglogBB X = log X = logBB X Xzz

Write the following logarithms as Write the following logarithms as 1 logarithm1 logarithm

1)1) loglog55 10 + log 10 + log55 6 6

2) log2) log44 6 + log 6 + log44 3 3

3) 3 log3) 3 log66 2 2

4) 2 log4) 2 log33 3 + log 3 + log33 4 4

5) (1/2)log5) (1/2)log22 25 + log 25 + log22 2 - log 2 - log22 5 5

6) 4 log6) 4 log33 3 + log 3 + log33 x - log x - log33 5 5

Evaluating LogsEvaluating Logs

Evaluate logEvaluate log7744just use your calculator…just use your calculator…The log with the base is The log with the base is ALWAYS THE ALWAYS THE DENOMINATOR!!! DENOMINATOR!!!

(log(4))/(log(7))(log(4))/(log(7))

Solving Logarithmic Solving Logarithmic EquationsEquations

loglog77n = (2/3)logn = (2/3)log7788

loglog66x + logx + log669 = log9 = log665454

loglog99(3x+14) – log(3x+14) – log995 = log5 = log99(2x)(2x)

loglog1010(3x – 5) + log(3x – 5) + log1010 x = log x = log101022

loglog1010 4 + log 4 + log1010x = 2x = 2

Solve each equation.Solve each equation.

Solve continued…Solve continued…