Solving Logarithmic Equations

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Presentation transcript:

Solving Logarithmic Equations

Solving an Exponential Equation Ex. 73x=20 log720=3x 1.5395≈3x x≈.5132 Write in log form Evaluate in the calculator Divide both sides by 3.

Solving an Exponential Equation Ex. 3x+4=101 log3101=x+4 4.2=x+4 0.2=x

Try these. Solve for x. Ex. 2x=3 Ex. 4x=19 Ex. 5-3x=-40 Ex. 14x+1=36

log b Change of Base Formula logbM=logM Ex. log315 Ex. log5400

Solving a Logarithmic Equation Ex. log(3x+1)=5 Ex. log(7-2x)=-1 105=3x+1 100,000=3x+1 99,999=3x 33,333=x 10-1=7-2x 0.1=7-2x -6.9=-2x 3.45=x

Solve for x. Ex. log 2x = -1 Ex. log (3x+1) = 2 Ex. log (5-2x) = 0 Ex. 3 log x = 1.5 x=.05 x=33 x=2 x=3.162

Using Logarithmic Properties to Solve an Equation Ex. 2logx-log3=2 Ex. log6-log3x=-2 log 6 = -2 3x 10-2 = 6 .01 = 6 .03x=6 x=200 logx2-log 3 = 2 log x2 =2 3 102=x2 100=x2 300=x2 x=17.32 or x=-17.32