Solving Exponential and Logarithmic Equations

Single Logarithms

100

Write the following logarithm as a single logarithm:

log₂4 + log₂2 - log₂8

log₂1 = 0

200

Expand the following logarithm:

log₆(3x²y)

log₆3 + 2log₆x + log₆y

300

Write the following logarithm as a single logarithm:

2log(x) - 3log(y)

log (x^2/y^3)

400

Expand the following logarithm:

log((x^4y^6)/z^3)

4log (x) + 6log(y) - 3log(z)

500

Write the following logarithm as a single logarithm:

log₅y - 4log₅r - 2log₅t

log_5(y/(r^4t^2))

Exponential Equations

100

Solve the following equation. Round to the nearest hundredth.

8ⁿ⁺¹ = 3

-0.47

200

Solve the following equation. Round to the nearest hundredth.

5^2x = 25

1

300

Solve the following equation. Round to the nearest hundredth.

5^x-2 = 11.18

3.50

400

Solve the following equation. Round to the nearest hundredth.

15^2n-3 = 3375

3

500

Solve the following equation. Round to the nearest hundredth.

2(5³ⁿ) = 31250

2

Logarithm Equations

100

Solve each equation.

log 4x = -1

1/40 or 0.025

200

Solve each equation.

log (x - 25) = 2 

125

300

Solve each equation.

4 log₂ x = 4

2

400

Solve each equation.

2 log₂8 + log₂x = 8

4

500

Solve each equation.

log₄(x)+log₄(x-12)=3

x=16