ASTB Math FREE Sample Practice Questions

7- C
\(|9 – (12 ÷ | 2 – 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5\)

8- D
METHOD ONE
\(log_{2}⁡x = 5\)
Apply logarithm rule: \(a = log_b⁡(b^a)\)
\(5 = log_2⁡(2^5) = log_2⁡(32)\)
\(log_2⁡x = log_2⁡(32)\)
When the logs have the same base: \(log_b⁡(f(x)) = log_b⁡(g(x))⇒ f(x) = g(x)\)
then: \(x = 32\)

METHOD TWO
We know that:
\(log_a⁡b=c⇒b=a^c \)
\(log_2⁡x=5⇒x=2^5=32\)

9- D
\(\frac{x^3}{16}\)
\(⇒\) reciprocal is: \(\frac{16}{x^3}\)

10- A
\(f(x) = ln (2x + 1)\)
\(y = ln (2x + 1)\)
Change variables \(x\) and \(y: x = ln (2y + 1)\)
solve: \(x = ln (2y + 1)\)
\(y = \frac{e^{x}-1}{2}=\frac{1}{2}(e^{x} – 1)\)

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