What is 1/2 ln(3.73)-ln(0.26) ?

The solution to 1/2 ln(3.73)-ln(0.26) is ln(7.42815…)

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simplify 1/2 ln(3.73)-ln(0.26)

simplify

\frac{1}{2} ln (3.73) - ln (0.26)

ln (7.42815 \dots)

Decimal Notation

2.00527 \dots

Solution steps

\frac{1}{2} ln (3.73) - ln (0.26)

Apply log rule:

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

\frac{1}{2} ln (3.73) = ln (3.7 3^{\frac{1}{2}})

= ln (3.7 3^{\frac{1}{2}}) - ln (0.26)

Apply log rule:

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

ln (3.7 3^{\frac{1}{2}}) - ln (0.26) = ln (\frac{3.7 3 ^{\frac{1}{2}}}{0.26})

= ln (\frac{3.7 3 ^{\frac{1}{2}}}{0.26})

\frac{3.7 3 ^{\frac{1}{2}}}{0.26} = 7.42815 \dots

= ln (7.42815 \dots)

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What is 1/2 ln(3.73)-ln(0.26) ?
The solution to 1/2 ln(3.73)-ln(0.26) is ln(7.42815…)