What is ln((10.25*10^{-12})/(16*10^{-15)}) ?

The solution to ln((10.25*10^{-12})/(16*10^{-15)}) is 3ln(10)-4ln(2)+ln(10.25)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((10.2510^{-12})/(1610^{-15)})

simplify

ln (\frac{10.25 \cdot 1 0 ^{- 12}}{16 \cdot 1 0 ^{- 15}})

3 ln (10) - 4 ln (2) + ln (10.25)

Decimal Notation

6.46244 \dots

Solution steps

ln (\frac{10.25 \cdot 1 0 ^{- 12}}{16 \cdot 1 0 ^{- 15}})

Apply log rule:

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

ln (\frac{10.25 \cdot 1 0 ^{- 12}}{16 \cdot 1 0 ^{- 15}}) = ln (10.25 \cdot 1 0^{- 12}) - ln (16 \cdot 1 0^{- 15})

= ln (1 0^{- 12} \cdot 10.25) - ln (1 0^{- 15} \cdot 16)

Apply log rule:

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

ln (10.25 \cdot 1 0^{- 12}) = ln (10.25) + ln (1 0^{- 12}), ln (16 \cdot 1 0^{- 15}) = ln (16) + ln (1 0^{- 15})

= ln (10.25) + ln (1 0^{- 12}) - (ln (16) + ln (1 0^{- 15}))

Apply log rule:

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

ln (1 0^{- 12}) = - 12 ln (10)

= ln (10.25) - 12 ln (10) - (ln (16) + ln (1 0^{- 15}))

Apply log rule:

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

ln (1 0^{- 15}) = - 15 ln (10)

= ln (10.25) - 12 ln (10) - (ln (16) - 15 ln (10))

ln (16) = 4 ln (2)

= ln (10.25) - 12 ln (10) - (4 ln (2) - 15 ln (10))

- (4 ln (2) - 15 ln (10)) : - 4 ln (2) + 15 ln (10)

= ln (10.25) - 12 ln (10) - 4 ln (2) + 15 ln (10)

Simplify

ln (10.25) - 12 ln (10) - 4 ln (2) + 15 ln (10) : 3 ln (10) - 4 ln (2) + ln (10.25)

= 3 ln (10) - 4 ln (2) + ln (10.25)

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

lo g_{7} (\frac{x ^{4}}{x - 8})

\frac{1}{3} lo g_{10} (x) - 2 lo g_{10} (y)

- \frac{3}{10} lo g_{2} (\frac{3}{10}) - \frac{7}{10} lo g_{2} (\frac{7}{10})

What is ln((10.25*10^{-12})/(16*10^{-15)}) ?
The solution to ln((10.25*10^{-12})/(16*10^{-15)}) is 3ln(10)-4ln(2)+ln(10.25)