What is 0.98ln(3)+0.02ln(2.3) ?

The solution to 0.98ln(3)+0.02ln(2.3) is ln(2.98410…)

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simplify 0.98ln(3)+0.02ln(2.3)

simplify

0.98 ln (3) + 0.02 ln (2.3)

ln (2.98410 \dots)

Decimal Notation

1.09329 \dots

Solution steps

0.98 ln (3) + 0.02 ln (2.3)

Apply log rule:

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

0.98 ln (3) = ln (3^{0.98})

= ln (3^{0.98}) + 0.02 ln (2.3)

Apply log rule:

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

0.02 ln (2.3) = ln (2. 3^{0.02})

= ln (3^{0.98}) + ln (2. 3^{0.02})

Apply log rule:

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

ln (3^{0.98}) + ln (2. 3^{0.02}) = ln (3^{0.98} \cdot 2. 3^{0.02})

= ln (3^{0.98} \cdot 2. 3^{0.02})

3^{0.98} \cdot 2. 3^{0.02} = 2.98410 \dots

= ln (2.98410 \dots)

\frac{7}{2} - 9 ln (4) + 9 ln (3)

ln (x) + ln (4 x)

ln (3 a) - ln (2 b)

5 lo g_{3} (q) + 2 lo g_{3} (y)

ln (\frac{z}{x - y})

What is 0.98ln(3)+0.02ln(2.3) ?
The solution to 0.98ln(3)+0.02ln(2.3) is ln(2.98410…)