What is 95/100*ln(5*10^6)+5/100*ln(1000) ?

The solution to 95/100*ln(5*10^6)+5/100*ln(1000) is (19ln(5)+117ln(10))/(20)

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simplify 95/100ln(510^6)+5/100*ln(1000)

simplify

\frac{95}{100} \cdot ln (5 \cdot 1 0^{6}) + \frac{5}{100} \cdot ln (1000)

\frac{19 ln ( 5 ) + 117 ln ( 10 )}{20}

Decimal Notation

14.99908 \dots

Solution steps

\frac{95}{100} ln (5 \cdot 1 0^{6}) + \frac{5}{100} ln (1000)

Apply log rule:

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

\frac{95}{100} ln (5 \cdot 1 0^{6}) = \frac{95}{100} ln (5) + \frac{95}{100} ln (1 0^{6})

= \frac{95}{100} ln (5) + \frac{95}{100} ln (1 0^{6}) + \frac{5}{100} ln (1000)

Apply log rule:

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

ln (1 0^{6}) = 6 ln (10)

= \frac{95}{100} ln (5) + \frac{95}{100} \cdot 6 ln (10) + \frac{5}{100} ln (1000)

\frac{95}{100} ln (5) = \frac{19 ln ( 5 )}{20}

\frac{95}{100} \cdot 6 ln (10) = \frac{57 ln ( 10 )}{10}

\frac{5}{100} ln (1000) = \frac{3 ln ( 10 )}{20}

= \frac{19 ln ( 5 )}{20} + \frac{57 ln ( 10 )}{10} + \frac{3 ln ( 10 )}{20}

Combine the fractions

\frac{19 ln ( 5 )}{20} + \frac{3 ln ( 10 )}{20} : \frac{19 ln ( 5 ) + 3 ln ( 10 )}{20}

= \frac{19 ln ( 5 ) + 3 ln ( 10 )}{20} + \frac{57 ln ( 10 )}{10}

Least Common Multiplier of

20, 10 : 20

Adjust Fractions based on the LCM

= \frac{19 ln ( 5 ) + 3 ln ( 10 )}{20} + \frac{114 ln ( 10 )}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{19 ln ( 5 ) + 3 ln ( 10 ) + 114 ln ( 10 )}{20}

Add similar elements:

3 ln (10) + 114 ln (10) = 117 ln (10)

= \frac{19 ln ( 5 ) + 117 ln ( 10 )}{20}

ln (\frac{x}{y}) - ln (\frac{a}{b})

ln (\frac{( x + 3 ) ^{2}}{e ^{x} x})

- \frac{1}{2} ln (5 - 2 x) - ln (x)

ln ∣ x ∣ + 2 ln (x^{2} + 4) + C

ln (\frac{10}{22.5})

What is 95/100*ln(5*10^6)+5/100*ln(1000) ?
The solution to 95/100*ln(5*10^6)+5/100*ln(1000) is (19ln(5)+117ln(10))/(20)