What is log_{10}(1/(5*10^{-3)}) ?

The solution to log_{10}(1/(5*10^{-3)}) is -(log_{10}(5)-3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{10}(1/(5*10^{-3)})

simplify

lo g_{10} (\frac{1}{5 \cdot 1 0 ^{- 3}})

- (lo g_{10} (5) - 3)

Decimal Notation

2.30102 \dots

Solution steps

lo g_{10} (\frac{1}{5 \cdot 1 0 ^{- 3}})

Apply log rule:

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

lo g_{10} (\frac{1}{5 \cdot 1 0 ^{- 3}}) = lo g_{10} (1) - lo g_{10} (5 \cdot 1 0^{- 3})

= lo g_{10} (1) - lo g_{10} (1 0^{- 3} \cdot 5)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (5 \cdot 1 0^{- 3}) = lo g_{10} (5) + lo g_{10} (1 0^{- 3})

= lo g_{10} (1) - (lo g_{10} (5) + lo g_{10} (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= lo g_{10} (1) - (lo g_{10} (5) - 3 lo g_{10} (10))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (lo g_{10} (5) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= 0 - (lo g_{10} (5) - 3)

0 - (lo g_{10} (5) - 3) = - (lo g_{10} (5) - 3)

= - (lo g_{10} (5) - 3)

\frac{( ln ( 2 ) - ln ( 3 ) )}{ln ( 3 ) - ln ( 2 )}

- lo g_{10} (2 x 1 0^{- 5})

2 (lo g_{7} (y) - 2 lo g_{7} (w)) + 3 lo g_{7} (z)

ln (\frac{10 π - 3 3}{6})

\frac{ln ( 2 ) - ln ( 3 )}{- ln ( 3 )}

What is log_{10}(1/(5*10^{-3)}) ?
The solution to log_{10}(1/(5*10^{-3)}) is -(log_{10}(5)-3)