Exercises for Question Type 5: Finding values of the base or the input of a log given one and an exponent

Question 1

Skill question

Find $b$ given $lo g_{3} (b) = 4$ .

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Question 2

Skill question

Find $x$ if $lo g_{\frac{1}{2}} (16) = x$ .

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Question 3

Skill question

Find $x$ if $lo g_{\frac{1}{3}} (27) = x$ .

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Question 4

Skill question

Solve for $x$ in $lo g_{5} (x) = 2$ .

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Question 5

Skill question

Find $x$ given $lo g_{4} (x) = \frac{1}{2}$ .

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Question 6

Skill question

Determine $b$ when $lo g_{b} (81) = 4$ .

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Question 7

Skill question

Solve for $a$ in $lo g_{a} (\frac{1}{125}) = 3$ .

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Question 8

Skill question

Solve for $x$ when $lo g_{x - 1} (9) = 2$ , given $x > 2$ .

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Question 9

Skill question

Determine $a$ when $lo g_{a} (8) = 3$ .

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Question 10

Skill question

Find $x$ if $lo g_{2} (x) = - 3$ .

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Question 11

Skill question

Find $x$ if $lo g_{2} (x - 1) = 4$ .

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Question 12

Skill question

Determine $x$ if $lo g_{x} (16) = 2$ .

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IB Mathematics Applications & Interpretation Question Type 5: Finding Values of the Base or the Input of a Log Given One and an Exponent Exercises