Question

solve: \\(\log_{2}(3x + 8) = 5\\)
which is an equivalent equation?
\\(2^5 = 3x + 8\\)
\\(5^2 = 3x + 8\\)
\\(2^5 = \log_{2}(3x + 8)^2\\)
\\(5^2 = \log_{2}(3x + 8)^5\\)

\\(x = \\)

solve: \\(\log_{x}64 = 3\\)
which is an equivalent equation?
\\(3^x = 64\\)
\\(x^3 = 64\\)
\\(64^x = 3\\)
\\(x^3 = 64^3\\)

Explanation:

Convert the first logarithmic equation to exponential form

Using the Logarithmic and Exponential Inverses knowledge point

$$ \log_{2}(3x + 8) = 5 \iff 2^5 = 3x + 8 $$

Solve the first equation for x

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK0
$$

Convert the second logarithmic equation to exponential form

Using the Logarithmic and Exponential Inverses knowledge point

$$ \log_{x}(64) = 3 \iff x^3 = 64 $$

Answer:

Question 1

• (A) \(2^5 = 3x + 8\) (Correct answer)
• (B) \(5^2 = 3x + 8\)
• (C) \(2^5 = [\log_{2}(3x + 8)]^2\)
• (D) \(5^2 = [\log_{2}(3x + 8)]^5\)

The solution is \(x =\) <blank>8</blank>.

Question 2

• (A) \(3^x = 64\)
• (B) \(x^3 = 64\) (Correct answer)
• (C) \(64^x = 3\)
• (D) \(x^3 = 64^3\)