What is 0.35^2(ln(6.65)+1.3(ln(6.01)-ln(6.65))) ?

The solution to 0.35^2(ln(6.65)+1.3(ln(6.01)-ln(6.65))) is 0.1225ln(5.83029…)

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simplify 0.35^2(ln(6.65)+1.3(ln(6.01)-ln(6.65)))

simplify

0.3 5^{2} (ln (6.65) + 1.3 (ln (6.01) - ln (6.65)))

0.1225 ln (5.83029 \dots)

Decimal Notation

0.21597 \dots

Solution steps

0.3 5^{2} (ln (6.65) + 1.3 (ln (6.01) - ln (6.65)))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (6.01) - ln (6.65) = ln (\frac{6.01}{6.65})

= 0.3 5^{2} (1.3 ln (\frac{6.01}{6.65}) + ln (6.65))

Divide the numbers:

\frac{6.01}{6.65} = 0.90375 \dots

= 0.3 5^{2} (ln (6.65) + 1.3 ln (0.90375 \dots))

Apply log rule:

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

1.3 ln (0.90375 \dots) = ln (0.90375 \dots^{1.3})

= 0.3 5^{2} (ln (6.65) + ln (0.90375 \dots^{1.3}))

Apply log rule:

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

ln (6.65) + ln (0.90375 \dots^{1.3}) = ln (6.65 \cdot 0.90375 \dots^{1.3})

= 0.3 5^{2} ln (6.65 \cdot 0.90375 \dots^{1.3})

6.65 \cdot 0.90375 \dots^{1.3} = 5.83029 \dots

= 0.3 5^{2} ln (5.83029 \dots)

0.3 5^{2} = 0.1225

= 0.1225 ln (5.83029 \dots)

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What is 0.35^2(ln(6.65)+1.3(ln(6.01)-ln(6.65))) ?
The solution to 0.35^2(ln(6.65)+1.3(ln(6.01)-ln(6.65))) is 0.1225ln(5.83029…)