Exponents and Logarithms

Solving Exponential Equations

100

Solve for x:

2^3x = 2⁶

What is 2?

200

Solve for x:

5^x = 125

What is 3?

300

Solve for x:

8^x-1 = 64

What is x = 3 ?

400

Solve for x:

(1/16) = 4^2x+6

What is x = -4 ?

500

Solve for x:

4^{2x - 8} = 1

 What is x = 4 ?

Rewriting Logarithms

100

Rewrite the following as a logarithm:

2⁵ = 32

What is log₂ 32 = 5 ?

200

Rewrite the following as an exponent:

log₃ 243 = 5

What is 3⁵ = 243 ?

300

Rewrite the following as a logarithm:

(1/2)^-3 = 8

What is log_(1/2) 8 = -3 ?

400

Rewrite the following as a logarithm:

e³ = 20.085...

What is ln(20.085...) = 3 ?

500

Rewrite the following as an exponent:

ln(5) = 1.609...

What is e^1.609... = 5 ?

Solving Logarithms:Powers Chart Only

100

Solve for x:

log₄ 64 = x

What is x = 3 ?

200

Solve for x:

log₃ (x + 4) = log₃ (2x - 4)

What is x = 8 ?

300

Solve for x:

log 4x = 3

What is x= 250 ?

400

Solve for x:

log₅ x - 3 = 1

 What is x = 625 ?

500

Solve for x:

3log₂ (2x +6) = 12

What is x = 5 ?

Expanding/Condensing Logarithms

100

Expand the following:

log_2 (xy)

What is log₂x + log₂y ?

200

Condense the following:

log 5 + log x + log y

What is log(5xy) ?

300

Expand the following:

log_2((3x)/y)

What is log₂ 3 + log₂ x - log₂ y ?

400

Condense the following:

log₃ 5 - log₃ x - log₃y

What is

log_3 (5/(xy))

 

500

Condense the following:

ln(1) - ln(5) - 3ln(x)

What is

ln(1/(5x^3))

Solving Logarithms with:Change of Base

100

Solve for x (round to the nearest thousandth):

2^x = 9

What is x = 3.170 ?

200

Solve for x (round to the nearest thousandth):

10^x + 5 = 130

What is x = 2.097 ?

300

Solve for x (round to the nearest thousandth):

5^(2x+5)-4=27

What is x = -1.433 ?

400

Solve for x (round to the nearest thousandth):

ln(x-5)-2=1

What is x = 25.086 ?

500

Solve for x (round to the nearest thousandth):

e^{2x + 3} = 52

What is x = 0.476 ?