What is (125*1.5*10^6)/(200*25*50)*ln(150/100) ?

The solution to (125*1.5*10^6)/(200*25*50)*ln(150/100) is 750(ln(150)-2ln(10))

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simplify (1251.510^6)/(2002550)*ln(150/100)

simplify

\frac{125 \cdot 1.5 \cdot 1 0 ^{6}}{200 \cdot 25 \cdot 50} \cdot ln (\frac{150}{100})

750 (ln (150) - 2 ln (10))

Decimal Notation

304.09883 \dots

Solution steps

\frac{125 \cdot 1.5 \cdot 1 0 ^{6}}{200 \cdot 25 \cdot 50} ln (\frac{150}{100})

Apply log rule:

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

ln (\frac{150}{100}) = ln (150) - ln (100)

= \frac{1 0 ^{6} \cdot 125 \cdot 1.5}{200 \cdot 25 \cdot 50} (ln (150) - ln (100))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{125 \cdot 1.5 \cdot 1 0 ^{6} ( ln ( 150 ) - ln ( 100 ) )}{200 \cdot 25 \cdot 50}

Multiply the numbers:

125 \cdot 1.5 = 187.5

= \frac{1 0 ^{6} \cdot 187.5 ( ln ( 150 ) - ln ( 100 ) )}{200 \cdot 25 \cdot 50}

Multiply the numbers:

200 \cdot 25 \cdot 50 = 250000

= \frac{1 0 ^{6} \cdot 187.5 ( ln ( 150 ) - ln ( 100 ) )}{250000}

Factor

1 0^{6} : 2^{6} \cdot 5^{6}

Factor

250000 : 5^{6} \cdot 2^{4}

= \frac{2 ^{6} \cdot 5 ^{6} \cdot 187.5 ( ln ( 150 ) - ln ( 100 ) )}{5 ^{6} \cdot 2 ^{4}}

Cancel

\frac{187.5 \cdot 2 ^{6} \cdot 5 ^{6} ( ln ( 150 ) - ln ( 100 ) )}{2 ^{4} \cdot 5 ^{6}} : 2^{2} \cdot 187.5 (ln (150) - ln (100))

= 2^{2} \cdot 187.5 (ln (150) - ln (100))

ln (100) = 2 ln (10)

= 2^{2} \cdot 187.5 (ln (150) - 2 ln (10))

2^{2} = 4

= 4 \cdot 187.5 (ln (150) - 2 ln (10))

Multiply the numbers:

4 \cdot 187.5 = 750

= 750 (ln (150) - 2 ln (10))

10 \cdot lo g_{10} (\frac{2.7 x 1 0 ^{- 11}}{1 0 ^{- 12}})

- \frac{1}{4} ln ∣ x + 2 ∣ + \frac{1}{4} ln ∣ x - 2 ∣

ln (2) + 2 (ln (2 + 2 - 1)) + ln (3)

\frac{1}{3} lo g_{3} (7) - lo g_{3} (2)

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

What is (125*1.5*10^6)/(200*25*50)*ln(150/100) ?
The solution to (125*1.5*10^6)/(200*25*50)*ln(150/100) is 750(ln(150)-2ln(10))