📈 Exponential Functions and Logarithms

Questions in this quiz

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1. Question 1

   Which expression is equivalent to $8^{2/3}$?

2. Question 2

   The function $f(x) = 2^{-x}$ represents exponential decay.

3. Question 3

   Solve for $x$: $\log_3(x) = 4$. The answer is $x =$ ___.

4. Question 4

   Which statement correctly converts the exponential equation $5^x = 125$ to logarithmic form?

5. Question 5

   The change of base formula states that $\log_b(x) = \frac{\log(x)}{\log(b)}$, where $\log$ denotes the common logarithm (base 10).

6. Question 6

   If $\ln(e^{2x}) = 8$, then $x =$ ___.

7. Question 7

   A bacterial culture doubles every 3 hours. If the initial population is 500 bacteria, what is the population after 9 hours?

8. Question 8

   For all positive real numbers $a$ and $b$ with $a \neq 1$, we have $\log_a(a) = 1$.

9. Question 9

   Solve $\log_2(x + 3) + \log_2(x - 1) = 4$ for $x$. Which value satisfies this equation?

10. Question 10

    Arrange these steps in order to solve the exponential equation $3^{2x-1} = 27$.