Lesson Worksheet: Logarithmic Functions Mathematics

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


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


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


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

  • A𝑔(𝑥)=𝑥21ln
  • B𝑔(𝑥)=12(𝑥1)ln
  • C𝑔(𝑥)=2𝑥1ln
  • D𝑔(𝑥)=(2𝑥1)ln
  • E𝑔(𝑥)=𝑥21ln


Make 𝑥 the subject of the equation 𝑦=2, assuming that 𝑎0.

  • A𝑥=(𝑦)𝑏𝑎log
  • B𝑥=(𝑦)𝑏log
  • C𝑥=(𝑦2)𝑏𝑎log
  • D𝑦=(𝑥)𝑏𝑎log
  • E𝑥=(𝑦)+𝑏𝑎log


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

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


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


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

  • A20
  • B1
  • C5
  • D9
  • E4


Consider the function 𝑓(𝑥)=(3𝑥1)log. If 𝑓(𝑎)=3, find the value of 𝑎.


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


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.

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