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What is the solution to the following equation?
A^-|x|
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Definition
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Term
What is the value of x?
log(A)x=B
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Definition
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What is the solution to this problem?
A^-B
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Definition
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Term
What is the solution to this problem?
1/(A^-B)
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Definition
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Term
What are the steps to solving this problem?
(A^(Bx+C))=D |
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Definition
1.)Take the Natural Log of Both Sides
ln(A^(Bx+C))=lnD
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2.)Use the Power Rule of Logarithms
(Bx+C)lnA=lnD
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3.)Use the Distributive Property
BxlnA+ClnA=lnD
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4.)Subtract ClnA from both sides
BxlnA=lnD-ClnA
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5.)Divide both sides by BlnA
x=(lnD-ClnA)/BlnA
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Term
What is the power rule of logarithms?
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Definition
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Term
How do you solve this exponential equation?
(A/(B-(C^x)))=D
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Definition
1.)Multiply both sides by (B-(C^x))
A=D(B-(C^x))
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2.)Distribute the D
A=DB-(D*(C^x))
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3.)Subtract DB from both sides
A-DB=-(D*(C^x))
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4.)Divide both sides by -D
(A-DB)/(-D)=(C^x)
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5.)Take the Natural Log of both sides
ln(A-DB)/(-D)=ln(C^x)
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6.)Use the Power Rule
ln(A-DB)/(-D)=xlnC
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7.)Divide both sides by lnC
(ln(A-DB)/(-D))/lnC=x
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8.)Use the Quotient Property
(ln(|A-DB|)-ln(|-D|))/lnC=x
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What is the solution to this logarithmic equation?
log[[x^2]-Ax-B]=0
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Definition
1.)Use the Quadratic Function on:
((x^2)-Ax(-B-1))
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2.)Your solution set is the solution set
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Term
What is the solution to this logarithmic equation?
log(A)[[x^2]-Bx+C]=1
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Definition
1.)Use the Quadratic Formula
[[x^2]-Bx+[C-A]]
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2.)Your Solution Set is the Solution Set
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Term
How do you write the equation in its logarithm form?
A^B=C
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Definition
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Term
How do you convert this to an exponential equation?
log(A)B=C
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Definition
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Term
How do you solve the logarithmic equation?
log(A)[x+B]-log(A)[x-C]=D
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Definition
1.)Apply Quotient Rule
log(a)[x+B/x-C]=D
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2.)Convert into an Exponential Expression
[x+B/x-C]=A^D
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3.)Multiply both sides by x-C
x+B=A^D(x-C)
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4.)Distribute
x+B=(A^D*x)-(A^D*C)
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5.)Subtract "x" from both sides
B=((A^D*x)-x)-(A^D*C)
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6.)Add (A^D*C) to both sides
B+(A^D*C)=((A^D*x)-x)
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7.)Divide both sides by (B+(A^D*C))
(B+(A^D*C))/((A^D*x)-x)
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