What is log_{10}((sqrt(B))/(10A)) ?

The solution to log_{10}((sqrt(B))/(10A)) is log_{10}(sqrt(B))-1-log_{10}(A)

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simplify log_{10}((sqrt(B))/(10A))

simplify

lo g_{10} (\frac{B}{10 A})

lo g_{10} (B) - 1 - lo g_{10} (A)

Solution steps

lo g_{10} (\frac{B}{10 A})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{B}{10 A}) = lo g_{10} (B) - lo g_{10} (10 A)

= lo g_{10} (B) - lo g_{10} (10 A)

Simplify

lo g_{10} (10 A) : 1 + lo g_{10} (A)

= lo g_{10} (B) - (1 + lo g_{10} (A))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{10} (A)) = - 1 - lo g_{10} (A)

= lo g_{10} (B) - 1 - lo g_{10} (A)

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What is log_{10}((sqrt(B))/(10A)) ?
The solution to log_{10}((sqrt(B))/(10A)) is log_{10}(sqrt(B))-1-log_{10}(A)