What is 0.7ln(35)+0.3ln(7.5) ?

The solution to 0.7ln(35)+0.3ln(7.5) is ln(22.04783…)

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simplify 0.7ln(35)+0.3ln(7.5)

simplify

0.7 ln (35) + 0.3 ln (7.5)

ln (22.04783 \dots)

Decimal Notation

3.09321 \dots

Solution steps

0.7 ln (35) + 0.3 ln (7.5)

Apply log rule:

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

0.7 ln (35) = ln (3 5^{0.7})

= ln (3 5^{0.7}) + 0.3 ln (7.5)

Apply log rule:

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

0.3 ln (7.5) = ln (7. 5^{0.3})

= ln (3 5^{0.7}) + ln (7. 5^{0.3})

Apply log rule:

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

ln (3 5^{0.7}) + ln (7. 5^{0.3}) = ln (3 5^{0.7} \cdot 7. 5^{0.3})

= ln (3 5^{0.7} \cdot 7. 5^{0.3})

3 5^{0.7} \cdot 7. 5^{0.3} = 22.04783 \dots

= ln (22.04783 \dots)

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What is 0.7ln(35)+0.3ln(7.5) ?
The solution to 0.7ln(35)+0.3ln(7.5) is ln(22.04783…)