What is sqrt((5(ln(5)-ln(2)))^2+(ln(5)-ln(2))^2) ?

The solution to sqrt((5(ln(5)-ln(2)))^2+(ln(5)-ln(2))^2) is sqrt(26)ln(5/2)

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simplify sqrt((5(ln(5)-ln(2)))^2+(ln(5)-ln(2))^2)

simplify

(5 (ln (5) - ln (2)))^{2} + (ln (5) - ln (2))^{2}

26 ln (\frac{5}{2})

Decimal

4.67218 \dots

Solution steps

(5 (ln (5) - ln (2)))^{2} + (ln (5) - ln (2))^{2}

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

5^{2} = 25

= 25 ln^{2} (\frac{5}{2}) + ln^{2} (\frac{5}{2})

Add similar elements:

25 ln^{2} (\frac{5}{2}) + ln^{2} (\frac{5}{2}) = 26 ln^{2} (\frac{5}{2})

= 26 ln^{2} (\frac{5}{2})

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= 26 ln^{2} (\frac{5}{2})

Apply radical rule:

n a^{n} = a,

assuming

a \geq 0

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

= 26 ln (\frac{5}{2})

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What is sqrt((5(ln(5)-ln(2)))^2+(ln(5)-ln(2))^2) ?
The solution to sqrt((5(ln(5)-ln(2)))^2+(ln(5)-ln(2))^2) is sqrt(26)ln(5/2)