Lesson Worksheet: Logarithmic Functions Mathematics • 10th Grade

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


If ๐‘”(๐‘ฅ) is the inverse of the function ๐‘“(๐‘ฅ)=2๏—๏Šฐ๏Šซ, find ๐‘”(๐‘ฅ).

  • A๐‘”(๐‘ฅ)=(๐‘ฅ)โˆ’2log๏Šซ
  • B๐‘”(๐‘ฅ)=(๐‘ฅ)โˆ’5log๏Šซ
  • C๐‘”(๐‘ฅ)=(๐‘ฅ)โˆ’5log๏Šจ
  • D๐‘”(๐‘ฅ)=(๐‘ฅ)+5log๏Šจ
  • E๐‘”(๐‘ฅ)=(๐‘ฅ)+2log๏Šซ


Consider the function ๐‘“(๐‘ฅ)=๐‘ฅlog๏Šฉ. Find the value of ๐‘“(9).


If ๐‘”(๐‘ฅ) is the inverse of the function ๐‘“(๐‘ฅ)=2๐‘’๏—๏Šฐ๏Šง, find ๐‘”(๐‘ฅ).

  • A๐‘”(๐‘ฅ)=๐‘ฅ2โˆ’1ln
  • B๐‘”(๐‘ฅ)=12(๐‘ฅโˆ’1)ln
  • C๐‘”(๐‘ฅ)=2๐‘ฅโˆ’1ln
  • D๐‘”(๐‘ฅ)=(2๐‘ฅโˆ’1)ln
  • E๐‘”(๐‘ฅ)=๏€ป๐‘ฅ2โˆ’1๏‡ln


Make ๐‘ฅ the subject of the equation ๐‘ฆ=2๏Œบ๏—๏Šฐ๏Œป, assuming that ๐‘Žโ‰ 0.

  • A๐‘ฅ=(๐‘ฆ)โˆ’๐‘๐‘Žlog๏Šจ
  • B๐‘ฅ=(๐‘ฆ)โˆ’๐‘log๏Šจ
  • C๐‘ฅ=(๐‘ฆโˆ’2)โˆ’๐‘๐‘Žlog
  • D๐‘ฆ=(๐‘ฅ)โˆ’๐‘๐‘Žlog๏Šจ
  • E๐‘ฅ=(๐‘ฆ)+๐‘๐‘Žlog๏Šจ


Find the solution set of the equation log๏Šซ125=๐‘ฅ+1.

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


The function ๐‘“(๐‘ฅ)=2๐‘’+3๏— has an inverse of the form ๐‘”(๐‘ฅ)=(๐‘Ž๐‘ฅ+๐‘)ln. What are the values of ๐‘Ž and ๐‘?

  • A๐‘Ž=12, ๐‘=โˆ’32
  • B๐‘Ž=โˆ’32, ๐‘=12
  • C๐‘Ž=12, ๐‘=32
  • D๐‘Ž=1, ๐‘=โˆ’3
  • E๐‘Ž=2, ๐‘=3


Given that the graph of the function ๐‘“(๐‘ฅ)=๐‘ฅlog๏Œบ passes through the point (1,024,5), find the value of ๐‘Ž.

  • A20
  • B1
  • C๏Žฃโˆš5
  • D9
  • E4


Consider the function ๐‘“(๐‘ฅ)=(3๐‘ฅโˆ’1)log๏Šจ. If ๐‘“(๐‘Ž)=3, find the value of ๐‘Ž.


Consider the function ๐‘“(๐‘ฅ)=๐‘๏—, where ๐‘ is a positive real number not equal to 1. What is the domain of ๐‘“(๐‘ฅ)๏Šฑ๏Šง?

  • AAll real numbers
  • B๐‘ฅ>๐‘
  • C0<๐‘ฅ<๐‘
  • D๐‘ฅ>0


The pH of a solution is given by the formula pHlog=โˆ’๏€บ๐‘Ž๏†๏‘๏H+, where ๐‘Ž๏‘๏H+ is the concentration of hydrogen ions. Determine the concentration of hydrogen ions in a solution whose pH is 8.4.

  • A10๏Šซ๏Ž–๏Šฌ
  • B10๏Šฑ๏Šซ๏Ž–๏Šฌ
  • C10๏Šฑ๏Šฎ๏Ž–๏Šช
  • D10๏Šฎ๏Ž–๏Šช

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