What is 5*ln(300)+3*ln(4.002)-ln(10^5)-1.1516 ?

The solution to 5*ln(300)+3*ln(4.002)-ln(10^5)-1.1516 is 5ln(300)+ln(0.00064…)-1.1516

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simplify 5ln(300)+3ln(4.002)-ln(10^5)-1.1516

simplify

5 \cdot ln (300) + 3 \cdot ln (4.002) - ln (1 0^{5}) - 1.1516

5 ln (300) + ln (0.00064 \dots) - 1.1516

Decimal Notation

20.01476 \dots

Solution steps

5 ln (300) + 3 ln (4.002) - ln (1 0^{5}) - 1.1516

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (4.002) = ln (4.00 2^{3})

= 5 ln (300) + ln (4.00 2^{3}) - ln (1 0^{5}) - 1.1516

Apply log rule:

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

ln (4.00 2^{3}) - ln (1 0^{5}) = ln (\frac{4.00 2 ^{3}}{1 0 ^{5}})

= 5 ln (300) + ln (\frac{4.00 2 ^{3}}{1 0 ^{5}}) - 1.1516

\frac{4.00 2 ^{3}}{1 0 ^{5}} = 0.00064 \dots

= 5 ln (300) + ln (0.00064 \dots) - 1.1516

\frac{43}{9} + ln (425) - ln (117)

ln (\frac{1 + 2 z}{1 - 2 z})

\frac{1}{3} ln (6 x^{2}) + ln (3 x)

5 ln (\frac{H - 5}{H + 3})

\frac{1}{2} ln (\frac{0.7}{0.3})

What is 5*ln(300)+3*ln(4.002)-ln(10^5)-1.1516 ?
The solution to 5*ln(300)+3*ln(4.002)-ln(10^5)-1.1516 is 5ln(300)+ln(0.00064…)-1.1516