What is 0.75*ln(10000)-0.25*ln(9000) ?

The solution to 0.75*ln(10000)-0.25*ln(9000) is ln(102.66900…)

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simplify 0.75ln(10000)-0.25ln(9000)

simplify

0.75 \cdot ln (10000) - 0.25 \cdot ln (9000)

ln (102.66900 \dots)

Decimal Notation

4.63151 \dots

Solution steps

0.75 ln (10000) - 0.25 ln (9000)

Apply log rule:

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

0.75 ln (10000) = ln (1000 0^{0.75})

= ln (1000 0^{0.75}) - 0.25 ln (9000)

Apply log rule:

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

0.25 ln (9000) = ln (900 0^{0.25})

= ln (1000 0^{0.75}) - ln (900 0^{0.25})

Apply log rule:

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

ln (1000 0^{0.75}) - ln (900 0^{0.25}) = ln (\frac{1000 0 ^{0.75}}{900 0 ^{0.25}})

= ln (\frac{1000 0 ^{0.75}}{900 0 ^{0.25}})

\frac{1000 0 ^{0.75}}{900 0 ^{0.25}} = 102.66900 \dots

= ln (102.66900 \dots)

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What is 0.75*ln(10000)-0.25*ln(9000) ?
The solution to 0.75*ln(10000)-0.25*ln(9000) is ln(102.66900…)