What is 2ln(6)-3/2 ln(5) ?

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

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simplify 2ln(6)-3/2 ln(5)

simplify

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

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

Decimal Notation

1.16936 \dots

Solution steps

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

Apply log rule:

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

2 ln (6) = ln (6^{2})

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

Apply log rule:

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

\frac{3}{2} ln (5) = ln (5^{\frac{3}{2}})

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

Apply log rule:

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

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

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

\frac{6 ^{2}}{5 ^{\frac{3}{2}}} = \frac{36 5}{25}

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

lo g_{2} (\frac{x}{3 y})

\frac{2}{3} lo g_{10} (\frac{x}{1 0 ^{4.4}})

lo g_{2} (5 ab)

4 lo g_{6} (r) - 3 lo g_{6} (s) - 2 lo g_{6} (t)

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