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I found an equation like this

$$5^2 \times 5^4 \times 5^6 \times 5^8 \times \cdots \times 5^{2n} = (0.008)^{-30}$$

Can someone explain me how to find the value of n in this equation.. I tried but couldn't get any result after sometime..

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1 Answer

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You have the equation is equivalent to $$5^2\times 5^4\times5^6\times\cdots\times5^{2n}=5^{90}$$ Combining the bases we have: $$5^x=5^{90}$$ where $$x=2\sum_{k=1}^nk=2\left(\frac{n(n+1)}{2}\right)=n(n+1)$$ I'll let you take it from here.

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