What is 4-5/2 ln(5)-11/8+5/2 ln(2) ?

The solution to 4-5/2 ln(5)-11/8+5/2 ln(2) is ln((4sqrt(10))/(125))+21/8

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simplify 4-5/2 ln(5)-11/8+5/2 ln(2)

simplify

4 - \frac{5}{2} ln (5) - \frac{11}{8} + \frac{5}{2} ln (2)

ln (\frac{4 10}{125}) + \frac{21}{8}

Decimal Notation

0.33427 \dots

Solution steps

4 - \frac{5}{2} ln (5) - \frac{11}{8} + \frac{5}{2} ln (2)

Apply log rule:

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

\frac{5}{2} ln (5) = ln (5^{\frac{5}{2}})

= 4 - ln (5^{\frac{5}{2}}) - \frac{11}{8} + \frac{5}{2} ln (2)

Apply log rule:

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

\frac{5}{2} ln (2) = ln (2^{\frac{5}{2}})

= 4 - ln (5^{\frac{5}{2}}) - \frac{11}{8} + ln (2^{\frac{5}{2}})

Apply log rule:

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

ln (2^{\frac{5}{2}}) - ln (5^{\frac{5}{2}}) = ln (\frac{2 ^{\frac{5}{2}}}{5 ^{\frac{5}{2}}})

= 4 + ln (\frac{2 ^{\frac{5}{2}}}{5 ^{\frac{5}{2}}}) - \frac{11}{8}

\frac{2 ^{\frac{5}{2}}}{5 ^{\frac{5}{2}}} = \frac{4 10}{125}

= 4 + ln (\frac{4 10}{125}) - \frac{11}{8}

Combine the fractions

4 - \frac{11}{8} : \frac{21}{8}

= ln (\frac{4 10}{125}) + \frac{21}{8}

lo g_{10} (\frac{x ^{2} - 4}{( x + 3 ) ^{2}})

- lo g_{10} (3.46 \cdot 1 0^{- 7})

ln (θ e^{(θ - 1) l n (x)})

ln (\frac{2 x - 3}{x ^{2} - 5 x})

(- \frac{1}{3}) ln (\frac{1}{3})

What is 4-5/2 ln(5)-11/8+5/2 ln(2) ?
The solution to 4-5/2 ln(5)-11/8+5/2 ln(2) is ln((4sqrt(10))/(125))+21/8