Logs,Surds and Exponentials

Logarithms

100

What are logarithms?

Logarithims is the inverse operation for exponentials.

200

Find the value of the following logarithms 

log₂ 32

𝒙 = 5

300

Convert to its equivalent logarithmic form

81 = 3⁴

4 = log₃ 81

400

Simplify to its single log form

log₂ 17 + log₂ 4

log₂ 68

500

Simplify to a single log form

log₂ 72 - log₂ 12

log₂ 6

Surds

100

Solve 

2√5 + 7√5 + 4√4

13√5

200

What are surds?

A way of using radical operation (√) to express an irrational number.

300

Solve 

2√2 × √3

2√6

400

Solve

2√20 × 2√40 × 2√2

320

500

Solve 

2√5 (3√2 + 7√3)

6√10 + 14√15

Exponentials

100

What is an exponential?

An exponential function is defined as y=a^𝒙

200

solve for 𝓧  

5^𝒙 = 1/125

𝒙 = -3

300

Solve for 𝓧

9^𝒙 = 243

𝒙 = 5/2

400

Solve for 𝓧

2(8^𝒙+2) = 16^𝒙+1

𝒙 = 3

500

8^𝒙 + 8^𝒙+1 = 576

𝒙 = 2