Question

identify the values of \\(a\\), \\(b\\), and \\(c\\) that make the statement below true.

\\(\log_{2}64 = 6\\) if and only if \\(a^b = c\\).

\\(a = 2\\)
\\(b = 6\\)
\\(c = 64\\)

which logarithmic equation is equivalent to \\(2^5 = 32\\)?

\\(\bigcirc\\) \\(\log_{2}32 = 5\\)
\\(\bigcirc\\) \\(\log_{5}32 = 2\\)
\\(\bigcirc\\) \\(\log_{32}5 = 2\\)
\\(\bigcirc\\) \\(\log_{2}5 = 32\\)

Explanation:

Convert logarithmic form to exponential form

Using the Logarithmic and Exponential Inverses knowledge point

$$ \log_{a}c = b \iff a^b = c $$

Applying this definition to \(\log_{2}64 = 6\):

$$ a = 2,\quad b = 6,\quad c = 64 $$

Convert exponential form to logarithmic form

Using the Logarithmic and Exponential Inverses knowledge point

$$ x^y = z \iff \log_{x}z = y $$

Applying this definition to \(2^5 = 32\):

$$ \log_{2}32 = 5 $$

Answer:

Question 1

The values are:
\(a =\) <blank>2</blank>
\(b =\) <blank>6</blank>
\(c =\) <blank>64</blank>

Question 2

• (A) \(\log_{2}32 = 5\) (Correct answer)
• (B) \(\log_{5}32 = 2\)
• (C) \(\log_{32}5 = 2\)
• (D) \(\log_{2}5 = 32\)