Exponential Equations

How can you solve an equation where the base of the exponentials are different, like 3^x and 9^(2x)?

• By converting both bases to a common base and then equating the exponents

• By adding the exponents together

• By subtracting the exponents

• By dividing one exponential by the other

Tags

CCSS.HSF.BF.B.5

What is the base conversion strategy used to solve 8^(4x) = 16^(5x-3)?

• Converting both sides to base 2

• Converting both sides to base 4

• Converting both sides to base 8

• Converting both sides to base 16

What is the result of 3 raised to the power of 1.8928?

• None of the above

• Approximately 8.00009

• Exactly 8

• Approximately 7.999

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

When solving an equation with e^x = 7, why is it preferable to use the natural log?

• None of the above

• Both A and B

• Because it simplifies to x directly

• Because the base of the natural log is e

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

What is the exact value of x when solving the equation ln(e^x) = ln(7)?

• x = 1.9459

• x = e^7

• x = 7

• x = ln(7)

Tags

CCSS.HSA.REI.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

What is the first step in solving the equation 5 + 4^(x-2) = 23?

• Multiplying both sides by 4

• Factoring the equation

• Taking the logarithm of both sides

• Subtracting 5 from both sides

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

What is the value of x when 4^(2x) * 4^(x) + 64 = 0?

• x = 4

• x = 0

• x = -1 and x = -2

• x = 1 and x = 2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

In the equation 3^(x^2 + 4x) = 1/27, what are the possible values of x?

• x = 0

• x = 3 and x = 1

• x = -3 and x = -1

• x = -4 and x = 1

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

How do you solve an equation where you have to factor by substitution?

• By setting a variable equal to a part of the equation

• By adding the exponents

• By dividing the equation

• By multiplying the bases

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

In the equation 3^(2x) - 3^(2x-1) = 18, what technique is used to simplify the equation?

• Factoring out the greatest common factor

• Converting to a common base

• Using logarithms

• Substitution

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3