Question

what is the solution of \\(\log(t-3) = \log(17-4t)\\)?

• 4
• 5
• 15
• 20

Explanation:

Equate the logarithmic arguments

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK0
$$

Solve the linear equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Verify the solution and domain

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK2
$$

Wait, looking closely at the image, the equation is:

$$ \log(t-3) = \log(17-4t) \text{ or } \log(17-t) \text{?} $$

Let's re-examine the image text:
"What is the solution of \(\log(t-3) = \log(17-4t)\)?" No, it looks like \(\log(17-t)\) but there is a \(4\)? No, it is \(\log(17-t)\)? Let's check the options: 4, 5, 15, 20.
If \(t=4\):
\(\log(4-3) = \log(1)\)
\(\log(17-4(4)) = \log(17-16) = \log(1)\).
Yes! The equation is:

$$ \log(t-3) = \log(17-4t) $$

Let's re-solve with this correct transcription:

$$ t - 3 = 17 - 4t $$

$$ 5t = 20 $$

$$ t = 4 $$

This perfectly matches the option \(4\).

Let's rewrite the steps with the correct equation:

Equate the logarithmic arguments

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK3
$$

Solve the linear equation

Using the Linear Equations knowledge point

$$
LATEXBLOCK4
$$

Verify the solution and domain

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK5
$$

Answer:

• (A) 4 (Correct answer)
• (B) 5
• (C) 15
• (D) 20