Lesson Worksheet: Logarithmic Functions Mathematics

Start Practising

In this worksheet, we will practice identifying, writing, and evaluating a logarithmic function as an inverse of the exponential function.

Q1:

If 𝑔(𝑥) is the inverse of the function 𝑓(𝑥)=2, find 𝑔(𝑥).

  • A𝑔(𝑥)=(𝑥)−2log
  • B𝑔(𝑥)=(𝑥)−5log
  • C𝑔(𝑥)=(𝑥)−5log
  • D𝑔(𝑥)=(𝑥)+5log
  • E𝑔(𝑥)=(𝑥)+2log

Q2:

Consider the function 𝑓(𝑥)=𝑥log. Find the value of 𝑓(9).

Q3:

If 𝑔(𝑥) is the inverse of the function 𝑓(𝑥)=2𝑒, find 𝑔(𝑥).

  • A𝑔(𝑥)=𝑥2−1ln
  • B𝑔(𝑥)=12(𝑥−1)ln
  • C𝑔(𝑥)=2𝑥−1ln
  • D𝑔(𝑥)=(2𝑥−1)ln
  • E𝑔(𝑥)=𝑥2−1ln

Q4:

Make 𝑥 the subject of the equation 𝑦=2, assuming that 𝑎≠0.

  • A𝑥=(𝑦)−𝑏𝑎log
  • B𝑥=(𝑦)−𝑏log
  • C𝑥=(𝑦−2)−𝑏𝑎log
  • D𝑦=(𝑥)−𝑏𝑎log
  • E𝑥=(𝑦)+𝑏𝑎log

Q5:

Find the solution set of the equation log125=𝑥+1.

  • A{5}
  • B{6}
  • C{4}
  • D{3}
  • E{2}

Q6:

The function 𝑓(𝑥)=2𝑒+3 has an inverse of the form 𝑔(𝑥)=(𝑎𝑥+𝑏)ln. What are the values of 𝑎 and 𝑏?

  • A𝑎=12, 𝑏=−32
  • B𝑎=−32, 𝑏=12
  • C𝑎=12, 𝑏=32
  • D𝑎=1, 𝑏=−3
  • E𝑎=2, 𝑏=3

Q7:

Given that the graph of the function 𝑓(𝑥)=𝑥log passes through the point (1,024,5), find the value of 𝑎.

  • A20
  • B1
  • C√5
  • D9
  • E4

Q8:

Consider the function 𝑓(𝑥)=(3𝑥−1)log. If 𝑓(𝑎)=3, find the value of 𝑎.

Q9:

Consider the function 𝑓(𝑥)=𝑏, where 𝑏 is a positive real number not equal to 1. What is the domain of 𝑓(𝑥)?

  • AAll real numbers
  • B𝑥>𝑏
  • C0<𝑥<𝑏
  • D𝑥>0

Q10:

The pH of a solution is given by the formula pHlog=−(𝑎)H+, where 𝑎H+ is the concentration of hydrogen ions. Determine the concentration of hydrogen ions in a solution whose pH is 8.4.

  • A10
  • B10
  • C10
  • D10

This lesson includes 33 additional questions and 153 additional question variations for subscribers.

GET YOUR PORTAL NOW

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.