Explain two non-verbal cues you would use to make the performance of the poem effective

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FURTHER LOGARITHMS

3. Find the value of $x$ given that $\log(15 - 5x) - 1 = \log(3x - 4)$ . (Assuming base 10 for $\log$ )

Express 1 as a logarithm with base 10.
$1 = \log_{10} 10$
Rewrite the equation.
$\log(15 - 5x) - \log 10 = \log(3x - 4)$
Apply the logarithm property $\log a - \log b = \log \left(\frac{a}{b}\right)$ on the left side.
$\log \left(\frac{15 - 5x}{10}\right) = \log(3x - 4)$
Equate the arguments of the logarithms.
$\frac{15 - 5x}{10} = 3x - 4$
Solve the resulting algebraic equation.
$15 - 5x = 10(3x - 4)$ $15 - 5x = 30x - 40$ $15 + 40 = 30x + 5x$ $55 = 35x$ $x = \frac{55}{35}$ $x = \frac{11}{7}$
Check for valid solutions.
The arguments of logarithms must be positive.
For $\log(15 - 5x)$ : $15 - 5x > 0 \implies 15 > 5x \implies x < 3$ .
For $\log(3x - 4)$ : $3x - 4 > 0 \implies 3x > 4 \implies x > \frac{4}{3}$ .
Our solution $x = \frac{11}{7} \approx 1.57$ . This value satisfies both $x < 3$ and $x > \frac{4}{3}$ .
$x = \boxed{\mathbf{\frac{11}{7}}}$

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