Exercises: Understand the Inverse Relationship Between Exponents and Logarithms

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Grade 9·21 problems·~30 min·Common Core Math - HS Functions·group·hsf-bf-b-5

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Warm-Up: Review What You Know

These problems review skills from earlier lessons.

Which function is the inverse of $f(x) = 3^x$ ?

$g(x) = x^3$

$g(x) = \log_3(x)$

$g(x) = \dfrac{1}{3^x}$

$g(x) = 3^{-x}$

What value of $y$ satisfies $2^y = 64$ ?

The graph of $y = 2^x$ and the graph of its inverse function are reflections over which line?

The $x$ -axis

The $y$ -axis

The line $y = x$

The line $y = 2x$

Which equation correctly rewrites $5^3 = 125$ in logarithmic form?

$\log_{125}(5) = 3$

$\log_5(125) = 3$

$\log_3(125) = 5$

$\log_5(3) = 125$

If $\log_3(x) = 4$ , what is $x$ ?

Evaluate $\log_2(32)$ .

$Round-trip chain diagram: start with 7, apply log base 10 to get the exponent, raise 10 to that power — the result is 7 again$

Simplify $10^{\log_{10}(7)}$ .

$\log_{10}(7)$

$10 \cdot \log_{10}(7)$

Simplify $\log_3(3^8)$ .

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