What is log_{10}(1/(10^{521)}) ?

The solution to log_{10}(1/(10^{521)}) is -521

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simplify log_{10}(1/(10^{521)})

simplify

lo g_{10} (\frac{1}{1 0 ^{521}})

- 521

Solution steps

lo g_{10} (\frac{1}{1 0 ^{521}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{1}{1 0 ^{521}}) = lo g_{10} (1) - lo g_{10} (1 0^{521})

= lo g_{10} (1) - lo g_{10} (1 0^{521})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{521}) = 521 lo g_{10} (10)

= lo g_{10} (1) - 521 lo g_{10} (10)

lo g_{10} (1) = 0

521 lo g_{10} (10) = 521

= 0 - 521

Simplify

= - 521

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