What is 20*log_{10}((10)/(2*10^{-5)}) ?

The solution to 20*log_{10}((10)/(2*10^{-5)}) is 20(1+log_{10}(50000))

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simplify 20log_{10}((10)/(210^{-5)})

simplify

20 \cdot lo g_{10} (\frac{10}{2 \cdot 1 0 ^{- 5}})

20 (1 + lo g_{10} (50000))

Decimal Notation

113.97940 \dots

Solution steps

20 lo g_{10} (\frac{10}{2 \cdot 1 0 ^{- 5}})

Apply log rule:

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

lo g_{10} (\frac{10}{2 \cdot 1 0 ^{- 5}}) = lo g_{10} (10) - lo g_{10} (2 \cdot 1 0^{- 5})

= 20 (lo g_{10} (10) - lo g_{10} (1 0^{- 5} \cdot 2))

Apply log rule:

lo g_{a} (a) = 1

= 20 (- lo g_{10} (1 0^{- 5} \cdot 2) + 1)

Multiply

2 \cdot 1 0^{- 5} : \frac{1}{50000}

= 20 (- lo g_{10} (\frac{1}{50000}) + 1)

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= 20 (- (- lo g_{10} (50000)) + 1)

Apply rule

- (- a) = a

= 20 (1 + lo g_{10} (50000))

ln (2 e^{- 3 x^{2}})

2 ln (\frac{82.6}{51.2})

- ln (1 - e^{λ}) - ln (y!)

ln (a^{n} \cdot e^{- a \cdot (x - b)})

lo g_{7} (x) + \frac{1}{2} lo g_{7} (y^{6}) - 2 lo g_{7} (z)

What is 20*log_{10}((10)/(2*10^{-5)}) ?
The solution to 20*log_{10}((10)/(2*10^{-5)}) is 20(1+log_{10}(50000))