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Popular >

simplify 1/2 ln(25)-ln(9)

Solution

simplify

\frac{1}{2} ln (25) - ln (9)

Solution

ln (\frac{5}{9})

+1

Decimal Notation

- 0.58778 \dots

Solution steps

\frac{1}{2} ln (25) - ln (9)

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 5^{\frac{1}{2}}) - ln (9)

Apply log rule:

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

ln (2 5^{\frac{1}{2}}) - ln (9) = ln (\frac{2 5 ^{\frac{1}{2}}}{9})

= ln (\frac{2 5 ^{\frac{1}{2}}}{9})

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

= ln (\frac{5}{9})

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Frequently Asked Questions (FAQ)

What is 1/2 ln(25)-ln(9) ?
The solution to 1/2 ln(25)-ln(9) is ln(5/9)