Logarithmic and Exponential Equations

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Multiple Choice

If 3^x = y, which of the following is true?

• log₃y = x

• log₃x = y

• log_xy = 3

• log_y3 = x

Multiple Choice

Rewrite in exponential form: 
2=log₉x

• 9^x=2

• 2^x=9

• 2⁹=x

• 9²=x

Multiple Choice

• 6log₈(xyz)

• log₈(x) - log₈(y) - 6log₈(z)

• log₈(x) + log₈(y) - log₈(z)

• log₈(x) + log₈(y) + 6log₈(z)

Multiple Choice

Condense the following logarithm: 3 log₂ x + 2 log₂ y – 4 log₂ z 

• log₂ x³y²∕z⁴

• log₂ x³y²z⁴

• log₂ xyz⁹

• 9log₂ xyz

Multiple Choice

• 5log₆(a) + 6log₆(c) − 30log₆(b)

• log₆(a) + 6log₆(c) − 5log₆(b)

• 6log₆(a) − 6log₆(c) − 30log₆(b)

• 6log₆(a) + 6log₆(c) − 30log₆(b)

Multiple Choice

If log_a8 = b, which of the following is true?

• a^b = 8

• b^a = 8

• a⁸ = b

• 8^b = a

Multiple Choice

Simplify log(12) + log (6)

• log(72)

• log(18)

• log(6)

• log(2)

Multiple Choice

Simplify: log(3) + 2log(5)

• log(75)

• 2log(15)

• log(30)

• log(13)

Multiple Choice

Simplify: 2log(x) + 3log(xy)

• log(x⁵y³)

• log(5xy)

• 5log(x²y)

• log(6x²y)

Multiple Choice

Simplify: log(16) - 3log(2)

• log(2)

• log(10)

• -3log(8)

• 3log(14)

Multiple Choice

Simplify: 3log(xy) - 2log(x)

• log(xy³)

• log(y)

• 1.5log(x²y)

• Can't be simplified

Multiple Choice

Simplify:
log_x(x³y) - log_x(xy)

• log_x(x²)

• 2

• log_x(x⁴-y²)

• x

​Exponential Equations

Multiple Choice

Solve

$$4^x=32.$$  

• $$x=\frac{3}{4}$$  

• $$x=\frac{2}{5}$$  

• $$x=\frac{5}{2}$$  

• $$x=\frac{1}{4}$$  

Multiple Choice

Solve

$$3^x=\frac{1}{27}.$$  

• $$x=-2$$  

• $$x=3$$  

• $$x=-3$$  

• $$x=9$$  

Multiple Choice

Solve

$$\left(\frac{1}{5}\right)^{-x}=25.$$  

• $$x=1$$  

• $$x=2$$  

• $$x=-1$$  

• $$x=-2$$  

Multiple Choice

Solve

$$27^x=81.$$  

• $$x=\frac{4}{3}$$  

• $$x=\frac{3}{4}$$  

• $$x=-\frac{4}{3}$$  

• $$x=-\frac{3}{4}$$  

Multiple Choice

Find the solution for

$$5^{\left(x+7\right)}=25^x.$$  

• $$x=2$$  

• $$x=-2$$  

• $$x=-7$$  

• $$x=7$$  

Multiple Choice

Solve

$$3\times2^x=24.$$  

• $$x=3$$  

• $$x=-3$$  

• $$x=2$$  

• $$x=-2$$  

Multiple Choice

Solve 3³ = 3^{4x + 2}

• x = ¼

• x = -¼

• x = ½

• x = -½

Multiple Choice

Solve: 7^-x = 49

• x = 1

• x = -1

• x = 2

• x = -2

Multiple Choice

Solve 8 = 2^5x+7

• x = ⅘

• x = ¼

• x = -⅘

• x = -¼

​LOGARITHMIC EQUATIONS

Multiple Choice

Solve

• 8

• -8

• 1/8

• -1/8

Multiple Choice

Solve

• 1

• -1

• 6

• -6

Multiple Choice

Solve

• 1/2

• -1/2

• 2

• -2

Multiple Choice

Solve

• 1/3

• -1/3

• -3

• 3

Multiple Choice

Solve

• 1/81

• -1/81

• -81

• 81

Multiple Choice

Solve

• -25

• 25

• 1/25

• -1/25

Multiple Choice

Solve

• 9

• -9

• 1/9

• -1/9

Multiple Choice

Solve

• 2

• -2

• 1/2

• -1/2

Multiple Choice

Solve

• 1

• 0

• -1

• Undefined

Multiple Choice

log₅(4x-7)=log₅(x+5)

• 3

• 12

• 4

• 7

Multiple Choice

log₄(3x-1)=log₄(2x+3)

• 4

• 3

• 1

• 8

Multiple Choice

log(2x) - log(5) = log(30)

• 6/5

• 45/2

• 75

• -3/8

Multiple Choice

log₉(x)+log₉(x+2)=log₉(35)

• 5

• -7

• 5, -7

• -7, -13

Multiple Choice

Solve log₅ (x + 3) = log₅ x + log₅ 3

• 3/2

• 9/2

• 2/3

• No Solution

Multiple Choice

Solve log₉ (x - 4) + log₉ (x + 1) = log₉ (x + 5) + log₉ (x - 6)

• 17/2

• -9/16

• 13

• -8

Multiple Choice

log₂(x+3)=4

• 16

• 13

• 3

• 10

Multiple Choice

log₈(4x+4)=2

• 15

• 12

• 10

• 3

Multiple Choice

Solve for x:
log(3x-1) - log(5) = 2

• x = 167

• x = 500

• x = 2

• x = 3.67