8 - Ms. Milani



Solving Logarithmic Equations NotesName _________________________________________Date __________________-452718755Property of Equality for Logarithmic EquationsIf b, x, and y are positive numbers with b≠1, then logbx=logby if and only if x = y.00Property of Equality for Logarithmic EquationsIf b, x, and y are positive numbers with b≠1, then logbx=logby if and only if x = y.Solve a logarithmic equation with a logarithm on both sides.EX1.1: log7(6x-16)=log7(x-1)EX1.2: log11=log(x2+2)center201402YOU TRY!Q1.1: ln(7x-13)=ln(2x+17)Q1.2: log8(x+6)=log8(4-x)00YOU TRY!Q1.1: ln(7x-13)=ln(2x+17)Q1.2: log8(x+6)=log8(4-x)Solve a logarithmic equation using the properties of logarithms.EX2.1: log7x-8+log72=log7(x-1)EX2.2: log2x+1-logx=log3+log4-159249176616YOU TRY!Q2.1: log82x+3+log8(4)=log8(4-x)Q2.2: logx+1-log10=log1000YOU TRY!Q2.1: log82x+3+log8(4)=log8(4-x)Q2.2: logx+1-log10=log10-513725685Identity Property of LogarithmsIf b≠0 and logab=c , then ac=b00Identity Property of LogarithmsIf b≠0 and logab=c , then ac=bRewrite the logarithmic function as an exponential function to solve the equation.EX3.1: log5(3x-8)=2EX3.2: log2(2x+5)=3-15924989870YOU TRY!Q3.1: log3(2x+9)=3Q3.2: log4(10x+624)=500YOU TRY!Q3.1: log3(2x+9)=3Q3.2: log4(10x+624)=5Solve a logarithmic equation using the properties of logarithms.EX4.1: log32x-1+log3(4)=1EX4.2: logx+2-log2x=2-15924981480YOU TRY!Q4.1: log23+log2(2x)=3Q4.2: log22x+3-log2(x)=300YOU TRY!Q4.1: log23+log2(2x)=3Q4.2: log22x+3-log2(x)=3 ................
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