What is (0.9)ln(8000)+(0.1)ln(7000) ?

The solution to (0.9)ln(8000)+(0.1)ln(7000) is ln(7893.88494…)

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simplify (0.9)ln(8000)+(0.1)ln(7000)

simplify

(0.9) ln (8000) + (0.1) ln (7000)

ln (7893.88494 \dots)

Decimal Notation

8.97384 \dots

Solution steps

(0.9) ln (8000) + (0.1) ln (7000)

Apply log rule:

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

(0.9) ln (8000) = ln (800 0^{(0.9)})

= ln (800 0^{(0.9)}) + (0.1) ln (7000)

Apply log rule:

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

(0.1) ln (7000) = ln (700 0^{(0.1)})

= ln (800 0^{(0.9)}) + ln (700 0^{(0.1)})

Apply log rule:

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

ln (800 0^{(0.9)}) + ln (700 0^{(0.1)}) = ln (800 0^{0.9} \cdot 700 0^{0.1})

= ln (800 0^{0.9} \cdot 700 0^{0.1})

800 0^{(0.9)} \cdot 700 0^{(0.1)} = 7893.88494 \dots

= ln (7893.88494 \dots)

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What is (0.9)ln(8000)+(0.1)ln(7000) ?
The solution to (0.9)ln(8000)+(0.1)ln(7000) is ln(7893.88494…)