What is (0.9)ln(5500)+(0.1)ln(4500) ?

The solution to (0.9)ln(5500)+(0.1)ln(4500) is ln(5390.73113…)

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simplify (0.9)ln(5500)+(0.1)ln(4500)

simplify

(0.9) ln (5500) + (0.1) ln (4500)

ln (5390.73113 \dots)

Solution steps

(0.9) ln (5500) + (0.1) ln (4500)

Apply log rule:

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

(0.9) ln (5500) = ln (550 0^{(0.9)})

= ln (550 0^{(0.9)}) + (0.1) ln (4500)

Apply log rule:

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

(0.1) ln (4500) = ln (450 0^{(0.1)})

= ln (550 0^{(0.9)}) + ln (450 0^{(0.1)})

Apply log rule:

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

ln (550 0^{(0.9)}) + ln (450 0^{(0.1)}) = ln (550 0^{0.9} \cdot 450 0^{0.1})

= ln (550 0^{0.9} \cdot 450 0^{0.1})

550 0^{(0.9)} \cdot 450 0^{(0.1)} = 5390.73113 \dots

= ln (5390.73113 \dots)

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What is (0.9)ln(5500)+(0.1)ln(4500) ?
The solution to (0.9)ln(5500)+(0.1)ln(4500) is ln(5390.73113…)