Given that (17)3y=735\left(\frac{1}{7}\right)^{3y} = 7^{\frac{3}{5}}, find the value of y. Ans: y = ___

Laws of indicesIndicesLinear one variable中文
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Worked solution

6

1. Express both sides using the same base

(17)3y=(7−1)3y=7−3y\left(\dfrac{1}{7}\right)^{3y}=\left(7^{-1}\right)^{3y}=7^{-3y}

So

7−3y=7357^{-3y}=7^{\frac{3}{5}}

2. Equate the indices and solve for $y$

Since the bases are the same,

−3y=35-3y=\dfrac{3}{5}

y=−35÷3=−15y=-\dfrac{3}{5}\div 3=-\dfrac{1}{5}

Answer

y=−15y=-\dfrac{1}{5}

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