What is 1/4 ln(10)+ln(13/4)-ln(9/2) ?

The solution to 1/4 ln(10)+ln(13/4)-ln(9/2) is ln((13\sqrt[4]{10})/(18))

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simplify 1/4 ln(10)+ln(13/4)-ln(9/2)

simplify

\frac{1}{4} ln (10) + ln (\frac{13}{4}) - ln (\frac{9}{2})

Decimal Notation

0.25022 \dots

Solution steps

\frac{1}{4} ln (10) + ln (\frac{13}{4}) - ln (\frac{9}{2})

Apply log rule:

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

\frac{1}{4} ln (10) = ln (1 0^{\frac{1}{4}})

= ln (1 0^{\frac{1}{4}}) + ln (\frac{13}{4}) - ln (\frac{9}{2})

Apply log rule:

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

ln (1 0^{\frac{1}{4}}) + ln (\frac{13}{4}) = ln (1 0^{\frac{1}{4}} \cdot \frac{13}{4})

= ln (1 0^{\frac{1}{4}} \cdot \frac{13}{4}) - ln (\frac{9}{2})

Apply log rule:

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

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What is 1/4 ln(10)+ln(13/4)-ln(9/2) ?
The solution to 1/4 ln(10)+ln(13/4)-ln(9/2) is ln((13\sqrt[4]{10})/(18))