Back to Tutor Intake Assessment: Understand inverse relationship of exponents and logarithms

HSF.BF.B.5 Tutor Intake — Logarithms as Inverses of Exponents

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Grade 9·11 problems·~13 min·Common Core Math - HS Functions·group·hsf-bf-b-5

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Concepts

Which statement best describes what $\log_2(8)$ means?

2 multiplied by 8

The exponent you put on 2 to get 8

The exponent you put on 8 to get 2

The square root of 8 in base 2

Which exponential equation is equivalent to $\log_5(125) = 3$ ?

$3^5 = 125$

$5^3 = 125$

$125^3 = 5$

$5^{125} = 3$

What is the value of $\log_b(1)$ for any valid base $b > 0$ , $b \ne 1$ ?

Enter your answer as a number.

Procedures

Evaluate $\log_3(81)$ .

Enter your answer as a number.

Evaluate $\log_2\!\left(\tfrac{1}{8}\right)$ .

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If $\log_b(x) = 4$ and $b = 10$ , what is $x$ ?

Enter your answer as a number.

Which expression equals $\log_4(4^7)$ ?

$4^7$

$7^4$

$\log_4(7)$

Simplify: $10^{\log_{10}(37)}$

$\log_{10}(37)$

$37$

$10 \times 37$

$10 + 37$

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