Question

which is the logarithmic form of \\(25 = 5^2\\)?
\\(\log_{2}5 = 25\\)
\\(\log_{25}2 = 5\\)
\\(\log_{5}25 = 2\\)
\\(\log_{5}2 = 25\\)

what is \\(\log_{3}9 = x\\) in exponential form?
\\(3^x = 9\\)
\\(9^x = 3\\)
\\(x^3 = 9\\)
\\(3^9 = x\\)

the equation \\(e^y = 2x\\) is equivalent to

Explanation:

Convert exponential to logarithmic form

Using the Logarithmic and Exponential Inverses knowledge point

$$ b^y = x \iff \log_b(x) = y $$

$$ 5^2 = 25 \iff \log_5(25) = 2 $$

Convert logarithmic to exponential form

Using the Logarithmic and Exponential Inverses knowledge point

$$ \log_b(x) = y \iff b^y = x $$

$$ \log_3(9) = x \iff 3^x = 9 $$

Convert natural exponential to natural logarithmic form

Using the Logarithmic and Exponential Inverses knowledge point

$$ e^y = 2x \iff \ln(2x) = y $$

Answer:

Question 1

• (A) \(\log_{2}5 = 25\)
• (B) \(\log_{25}2 = 5\)</mcq-correct>
• (C) \(\log_{5}25 = 2\) (Correct answer)

<mcq-option>(D) \(\log_{5}2 = 25\)

Question 2

• (A) \(3^x = 9\) (Correct answer)
• (B) \(9^x = 3\)
• (C) \(x^3 = 9\)
• (D) \(3^9 = x\)

Question 3

The equation \(e^y = 2x\) is equivalent to <blank>\(\ln(2x) = y\)</blank> (or \(\log_e(2x) = y\)).