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Popular >

simplify log_{2^{500}}(2^{1000})

Solution

simplify

lo g_{2^{500}} (2^{1000})

Solution

2

Solution steps

lo g_{2^{500}} (2^{1000})

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{500}} (2^{1000}) = \frac{1}{500} lo g_{2} (2^{1000})

= \frac{1}{500} lo g_{2} (2^{1000})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{2} (2^{1000}) = 1000

= \frac{1}{500} \cdot 1000

\frac{1}{500} \cdot 1000 = 2

= 2

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Frequently Asked Questions (FAQ)

What is log_{2^{500}}(2^{1000}) ?
The solution to log_{2^{500}}(2^{1000}) is 2