What is 4ln(2)-1/2 ln(25) ?

The solution to 4ln(2)-1/2 ln(25) is ln(16/5)

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simplify 4ln(2)-1/2 ln(25)

simplify

4 ln (2) - \frac{1}{2} ln (25)

ln (\frac{16}{5})

Decimal Notation

1.16315 \dots

Solution steps

4 ln (2) - \frac{1}{2} ln (25)

Apply log rule:

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

4 ln (2) = ln (2^{4})

= ln (2^{4}) - \frac{1}{2} ln (25)

Apply log rule:

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

\frac{1}{2} ln (25) = ln (2 5^{\frac{1}{2}})

= ln (2^{4}) - ln (2 5^{\frac{1}{2}})

Apply log rule:

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

ln (2^{4}) - ln (2 5^{\frac{1}{2}}) = ln (\frac{2 ^{4}}{2 5 ^{\frac{1}{2}}})

= ln (\frac{2 ^{4}}{2 5 ^{\frac{1}{2}}})

\frac{2 ^{4}}{2 5 ^{\frac{1}{2}}} = \frac{16}{5}

= ln (\frac{16}{5})

10 lo g_{10} (\frac{S}{1 0 ^{- 12}})

ln (\frac{67}{150})

lo g_{4} (\frac{c}{64})

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

2 ln (x) - 3 ln (y) - 4 ln (z)