taiwan-gsat 2024 Q7

taiwan-gsat · Other · gsat__math-a 5 marks Laws of Logarithms Verify Truth of Logarithmic Statements

Let $\Gamma$ be the graph formed by points $(x, y)$ satisfying $y = \log x$ on the coordinate plane. Which of the following relationships produce graphs that are completely identical to $\Gamma$?
(1) $y + \frac{1}{2} = \log(5x)$
(2) $2y = \log\left(x^{2}\right)$
(3) $3y = \log\left(x^{3}\right)$
(4) $x = 10^{y}$
(5) $x^{3} = 10^{\left(y^{3}\right)}$

Let $\Gamma$ be the graph formed by points $(x, y)$ satisfying $y = \log x$ on the coordinate plane. Which of the following relationships produce graphs that are completely identical to $\Gamma$?\\
(1) $y + \frac{1}{2} = \log(5x)$\\
(2) $2y = \log\left(x^{2}\right)$\\
(3) $3y = \log\left(x^{3}\right)$\\
(4) $x = 10^{y}$\\
(5) $x^{3} = 10^{\left(y^{3}\right)}$

Paper Questions

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