What is log_{10}(x/(10^{-12)}) ?

The solution to log_{10}(x/(10^{-12)}) is log_{10}(x)+12

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simplify log_{10}(x/(10^{-12)})

simplify

lo g_{10} (\frac{x}{1 0 ^{- 12}})

lo g_{10} (x) + 12

Solution steps

lo g_{10} (\frac{x}{1 0 ^{- 12}})

Simplify

\frac{x}{1 0 ^{- 12}} : x \cdot 1 0^{12}

= lo g_{10} (x \cdot 1 0^{12})

Apply log rule:

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

lo g_{10} (x \cdot 1 0^{12}) = lo g_{10} (x) + lo g_{10} (1 0^{12})

= lo g_{10} (x) + lo g_{10} (1 0^{12})

Apply log rule:

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

lo g_{10} (1 0^{12}) = 12

= lo g_{10} (x) + 12

ln (1 \cdot 5)

lo g_{5} (7) + lo g_{5} (6)

7 lo g_{b} (y) - \frac{1}{3} lo g_{b} (x) + 5 lo g_{b} (z)

- lo g_{10} (9 \times 1 0^{- 5})

ln (\frac{1}{2} (1 + e^{- x}))

What is log_{10}(x/(10^{-12)}) ?
The solution to log_{10}(x/(10^{-12)}) is log_{10}(x)+12