What is 3/4 ln(10000)+1/4 ln(9000) ?

The solution to 3/4 ln(10000)+1/4 ln(9000) is ln(1000*9000^{1/4})

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simplify 3/4 ln(10000)+1/4 ln(9000)

simplify

\frac{3}{4} ln (10000) + \frac{1}{4} ln (9000)

ln (1000 \cdot 900 0^{\frac{1}{4}})

Decimal Notation

9.18400 \dots

Solution steps

\frac{3}{4} ln (10000) + \frac{1}{4} ln (9000)

Apply log rule:

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

\frac{3}{4} ln (10000) = ln (1000 0^{\frac{3}{4}})

= ln (1000 0^{\frac{3}{4}}) + \frac{1}{4} ln (9000)

Apply log rule:

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

\frac{1}{4} ln (9000) = ln (900 0^{\frac{1}{4}})

= ln (1000 0^{\frac{3}{4}}) + ln (900 0^{\frac{1}{4}})

Apply log rule:

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

ln (1000 0^{\frac{3}{4}}) + ln (900 0^{\frac{1}{4}}) = ln (1000 0^{\frac{3}{4}} \cdot 900 0^{\frac{1}{4}})

= ln (1000 0^{\frac{3}{4}} \cdot 900 0^{\frac{1}{4}})

1000 0^{\frac{3}{4}} = 1000

= ln (1000 \cdot 900 0^{\frac{1}{4}})

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10 lo g_{10} (\frac{5 \cdot 1 0 ^{- 8}}{1 0 ^{- 12}})

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What is 3/4 ln(10000)+1/4 ln(9000) ?
The solution to 3/4 ln(10000)+1/4 ln(9000) is ln(1000*9000^{1/4})