What is ln((36sqrt(5))/(25)) ?

The solution to ln((36sqrt(5))/(25)) is 2ln(6)-3/2 ln(5)

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simplify ln((36sqrt(5))/(25))

simplify

ln (\frac{36 5}{25})

2 ln (6) - \frac{3}{2} ln (5)

Decimal Notation

1.16936 \dots

Solution steps

ln (\frac{36 5}{25})

Apply log rule:

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

ln (\frac{36 5}{25}) = ln (365) - ln (25)

= ln (365) - ln (25)

Apply log rule:

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

ln (365) = ln (36) + ln (5)

= ln (36) + ln (5) - ln (25)

ln (5) = \frac{1}{2} ln (5)

= ln (36) + \frac{1}{2} ln (5) - ln (25)

ln (36) = 2 ln (6)

ln (25) = 2 ln (5)

= 2 ln (6) + \frac{1}{2} ln (5) - 2 ln (5)

Add similar elements:

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

= 2 ln (6) - \frac{3}{2} ln (5)

lo g_{8} ((\frac{u ^{3}}{v})^{2})

ln (\frac{x}{e ^{4 x}})

ln (\frac{e ^{8}}{15})

- \frac{1}{4} \cdot lo g_{2} (\frac{1}{4}) - \frac{3}{4} \cdot lo g_{2} (\frac{3}{4})

What is ln((36sqrt(5))/(25)) ?
The solution to ln((36sqrt(5))/(25)) is 2ln(6)-3/2 ln(5)