Solving Exponential and Logarithmic Equations

Single Logarithms

100

Write the following logarithm as a single logarithm:

log₂4 + log₂2 - log₂8

log₂1

200

Write the following logarithm as a single logarithm:

log₆3 - log₆6

log_6 (1/2)

300

Write the following logarithm as a single logarithm:

2log(x) - 3log(y)

log (x^2/y^3)

400

Write the following logarithm as a single logarithm:

3(4log(t^2))

log (t²⁴)

500

Write the following logarithm as a single logarithm:

log₅y - 4(log₅r + 2log₅t)

log_5(y/(r^4t^8))

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 = 20

0.93

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 = 245

2.52

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 log x = 4

10

400

Solve each equation.

2 log (2x + 5) = 4

95/2

500

Solve each equation.

log₄(x²−2x)=log₄(5x−12)

x=3,x=4

Exponential with base e

100

Use natural logarithm to solve the following equation. Round your answer to the nearest hundredth.

e^x = 15

2.71

200

Use natural logarithm to solve the following equation. Round your answer to the nearest hundredth.

6 - e^12x = 5.2

-0.02

300

Use natural logarithm to solve the following equation. Round your answer to the nearest hundredth.

e^x-4 = 2

4.69

400

Use natural logarithm to solve the following equation. Round your answer to the nearest hundredth.

e^(x/5) = 32

17.33

500

Use natural logarithm to solve the following equation. Round your answer to the nearest hundredth.

5e^6x+3 = 0.1

-1.15

Natural Log. Equations

100

Solve each equation. Round your answer to the nearest hundredth.

ln e^x+5= 17

12

200

Solve each equation. Round your answer to the nearest hundredth.

ln x - ln 5 = -1

1.84

300

Solve each equation. Round your answer to the nearest hundredth.

3 - 4 ln (8x + 1) = 12

-0.11

400

Solve each equation. Round your answer to the nearest ten-thousandth place.

4 ln w+6 =12

4.4817

500

Solve each equation. Round your answer to the nearest hundredth.

ln(x²−1)=ln 24 - 1/2 ln 9

x = {-3,3}