Question 77

$$3^a = 5^b = 75^c \Rightarrow c(2a + b) =$$

Solution

$$3^a = 5^b = 75^c = k$$

$$3 = k^{\frac{1}{a}}, 5 = k^{\frac{1}{b}}, 75 = k^{\frac{1}{c}}$$

$$75 = 3 \times 5^2$$

$$k^{\frac{1}{c}} = k^{\frac{1}{a}} \times k^{\frac{2}{b}}$$

$$\frac{1}{c} = \frac{1}{a} + \frac{2}{b}$$

$$c = \frac{ab}{2a + b}$$

$$c(2a + b) = ab$$

Hence the answer is option B

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