Exercises for Question Type 5: Finding other values of logarithm

Question 1

Skill question

Given $lo g_{b} \frac{1}{16} = - 4$ (with $b > 0$ , $b \neq = 1$ ), find $b$ .

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Question 2

Skill question

Given $lo g_{a} 8 = 3$ , find $a$ (assume $a > 0$ and $a \neq = 1$ ).

[2]

Question 3

Skill question

Given $lo g_{x} 2 = \frac{1}{6}$ (with $x > 0$ , $x \neq = 1$ ), find $x$ .

[3]

Question 4

Skill question

Given $lo g_{a} b = \frac{p}{q}$ with $a > 0$ , $a \neq = 1$ , express $b$ in terms of $a$ , $p$ , and $q$ (assume $q \neq = 0$ ).

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Question 5

Skill question

Given $lo g_{\frac{1}{2}} x = - 3$ , find $x$ .

[2]

Question 6

Skill question

Given $lo g_{3} b = 4$ , find $b$ .

[2]

Question 7

Skill question

Given $lo g_{x - 1} 16 = 4$ and $x > 1$ , find $x$ .

[3]

Question 8

Skill question

Given $lo g_{3 x} y = 2$ with $x > 0$ , $x \neq = 1$ , $y > 0$ , express $y$ in terms of $x$ .

[4]

Question 9

Skill question

Given $lo g_{a} 27 = \frac{3}{2}$ , find $a$ (assume $a > 0$ , $a \neq = 1$ ).

[3]

Question 10

Skill question

Given $lo g_{a} 16 = 4$ (with $a > 0$ , $a \neq = 1$ ), find $a$ .

[3]

Question 11

Skill question

Given $lo g_{3 x} 81 = 2$ with $x > 0$ , find $x$ .

[4]

Question 12

Skill question

Given $lo g_{x} 81 = 4$ (with $x > 0$ and $x \neq = 1$ ), find $x$ .

[2]

IB Mathematics Analysis and Approaches Question Type 5: Finding Other Values of Logarithm Exercises