What is 5ln(b/(24))+6ln(b/(30))+9ln(b/(40)) ?

The solution to 5ln(b/(24))+6ln(b/(30))+9ln(b/(40)) is ln((b^{20})/(40^9*5.80475E15))

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simplify 5ln(b/(24))+6ln(b/(30))+9ln(b/(40))

simplify

5 ln (\frac{b}{24}) + 6 ln (\frac{b}{30}) + 9 ln (\frac{b}{40})

ln (\frac{b ^{20}}{4 0 ^{9} \cdot 5.80475 E 15})

Solution steps

5 ln (\frac{b}{24}) + 6 ln (\frac{b}{30}) + 9 ln (\frac{b}{40})

Apply log rule:

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

5 ln (\frac{b}{24}) = ln ((\frac{b}{24})^{5})

= ln ((\frac{b}{24})^{5}) + 6 ln (\frac{b}{30}) + 9 ln (\frac{b}{40})

Apply log rule:

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

6 ln (\frac{b}{30}) = ln ((\frac{b}{30})^{6})

= ln ((\frac{b}{24})^{5}) + ln ((\frac{b}{30})^{6}) + 9 ln (\frac{b}{40})

Apply log rule:

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

ln ((\frac{b}{24})^{5}) + ln ((\frac{b}{30})^{6}) = ln ((\frac{b}{30})^{6} (\frac{b}{24})^{5})

= ln ((\frac{b}{30})^{6} (\frac{b}{24})^{5}) + 9 ln (\frac{b}{40})

Simplify

(\frac{b}{24})^{5} (\frac{b}{30})^{6} : \frac{b ^{11}}{5.80475 E 15}

= ln (\frac{b ^{11}}{5.80475 E 15}) + 9 ln (\frac{b}{40})

Apply log rule:

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

9 ln (\frac{b}{40}) = ln ((\frac{b}{40})^{9})

= ln (\frac{b ^{11}}{5.80475 E 15}) + ln ((\frac{b}{40})^{9})

Apply log rule:

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

ln (\frac{b ^{11}}{5.80475 E 15}) + ln ((\frac{b}{40})^{9}) = ln ((\frac{b}{40})^{9} \frac{b ^{11}}{5.80475 E 15})

= ln ((\frac{b}{40})^{9} \frac{b ^{11}}{5.80475 E 15})

Simplify

\frac{b ^{11}}{5.80475 E 15} (\frac{b}{40})^{9} : \frac{b ^{20}}{4 0 ^{9} \cdot 5.80475 E 15}

= ln (\frac{b ^{20}}{4 0 ^{9} \cdot 5.80475 E 15})

ln (\frac{3}{2.9})

ln (5 x sin (x))

- 0.01386 \cdot ln (\frac{523}{298}) - 0.19867

\frac{( ln ( 7 ) - ln ( 3 ) )}{( 1.33 - 0.926 )}

ln (- 4.007 \cdot 1 0^{- 8})

What is 5ln(b/(24))+6ln(b/(30))+9ln(b/(40)) ?
The solution to 5ln(b/(24))+6ln(b/(30))+9ln(b/(40)) is ln((b^{20})/(40^9*5.80475E15))