What is log_{10}(1/(ab)) ?

The solution to log_{10}(1/(ab)) is -log_{10}(a)-log_{10}(b)

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simplify log_{10}(1/(ab))

simplify

lo g_{10} (\frac{1}{ab})

- lo g_{10} (a) - lo g_{10} (b)

Solution steps

lo g_{10} (\frac{1}{ab})

Simplify

\frac{1}{ab} : (ab)^{- 1}

= lo g_{10} ((ab)^{- 1})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} ((ab)^{- 1}) = - 1 \cdot lo g_{10} (ab)

= - 1 \cdot lo g_{10} (ab)

Apply rule:

1 \cdot a = a

= - lo g_{10} (ab)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

- lo g_{10} (ab) = - (lo g_{10} (a) + lo g_{10} (b))

= - (lo g_{10} (a) + lo g_{10} (b))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (a) + lo g_{10} (b)) = - lo g_{10} (a) - lo g_{10} (b)

= - lo g_{10} (a) - lo g_{10} (b)

- 4 ln (2 x)

- \frac{5 ln ( 50 )}{ln ( 2 )}

3.17 + lo g_{10} (\frac{0.34}{0.16})

ln (3) - ln (x)

2 lo g_{b} (u) + 9 lo g_{b} (v)

What is log_{10}(1/(ab)) ?
The solution to log_{10}(1/(ab)) is -log_{10}(a)-log_{10}(b)