What is ln((3.16*10^{-4})/(1.14*10^{-4)}) ?

The solution to ln((3.16*10^{-4})/(1.14*10^{-4)}) is ln(3.16)-ln(1.14)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((3.1610^{-4})/(1.1410^{-4)})

simplify

ln (\frac{3.16 \cdot 1 0 ^{- 4}}{1.14 \cdot 1 0 ^{- 4}})

ln (3.16) - ln (1.14)

Decimal Notation

1.01954 \dots

Solution steps

ln (\frac{3.16 \cdot 1 0 ^{- 4}}{1.14 \cdot 1 0 ^{- 4}})

Apply log rule:

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

ln (\frac{3.16 \cdot 1 0 ^{- 4}}{1.14 \cdot 1 0 ^{- 4}}) = ln (3.16 \cdot 1 0^{- 4}) - ln (1.14 \cdot 1 0^{- 4})

= ln (1 0^{- 4} \cdot 3.16) - ln (1 0^{- 4} \cdot 1.14)

Apply log rule:

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

ln (3.16 \cdot 1 0^{- 4}) = ln (3.16) + ln (1 0^{- 4}), ln (1.14 \cdot 1 0^{- 4}) = ln (1.14) + ln (1 0^{- 4})

= ln (3.16) + ln (1 0^{- 4}) - (ln (1.14) + ln (1 0^{- 4}))

Apply log rule:

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

ln (1 0^{- 4}) = - 4 ln (10)

= ln (3.16) - 4 ln (10) - (ln (1.14) - 4 ln (10))

Apply log rule:

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

ln (1 0^{- 4}) = - 4 ln (10)

= ln (3.16) - 4 ln (10) - (ln (1.14) - 4 ln (10))

- (ln (1.14) - 4 ln (10)) : - ln (1.14) + 4 ln (10)

= ln (3.16) - 4 ln (10) - ln (1.14) + 4 ln (10)

Simplify

ln (3.16) - 4 ln (10) - ln (1.14) + 4 ln (10) : ln (3.16) - ln (1.14)

= ln (3.16) - ln (1.14)

4 lo g_{a} (6 x + 1) + \frac{1}{4} lo g_{a} (x + 3)

\frac{( ln ( 42520 ) - ln ( 32301 ) )}{( 2010 - 2000 )}

lo g_{8} (\frac{- \frac{1}{2}}{3 - 5 x ^{2}})

lo g_{10} (9^{15})

lo g_{e} (7 x)

What is ln((3.16*10^{-4})/(1.14*10^{-4)}) ?
The solution to ln((3.16*10^{-4})/(1.14*10^{-4)}) is ln(3.16)-ln(1.14)