5)
$$7^a = 17,640,000$$
$$7^a = 7^2 \cdot 24^2 \cdot 25^2$$
จาก
$$7^a = 24^b \Rightarrow 7^{\frac{a}{b}} = 24$$
$$7^a = 25^c \Rightarrow 7^{\frac{a}{c}} = 25$$
แทนค่า
$$7^a = 7^2 \cdot 7^{\frac{2a}{b}} \cdot 7^{\frac{2a}{c}}$$
$$7^a = 7^{2(1+\frac{a}{b}+\frac{a}{c})}$$
$$a = 2(1+\frac{a}{b}+\frac{a}{c})$$
$$\frac{1}{2} = \frac{1}{a}+\frac{1}{b}+\frac{1}{c}$$
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