What is simplify-364/1740-1.144-ln(1.10066)+0.5ln(2) ?

The solution to simplify-364/1740-1.144-ln(1.10066)+0.5ln(2) is -91/435-1.144+ln(1.28487…)

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simplify-364/1740-1.144-ln(1.10066)+0.5ln(2)

simplify

- \frac{364}{1740} - 1.144 - ln (1.10066) + 0.5 ln (2)

- \frac{91}{435} - 1.144 + ln (1.28487 \dots)

Decimal Notation

- 1.10253 \dots

Solution steps

- \frac{364}{1740} - 1.144 - ln (1.10066) + 0.5 ln (2)

Apply log rule:

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

0.5 ln (2) = ln (2^{0.5})

= - \frac{364}{1740} - 1.144 - ln (1.10066) + ln (2^{0.5})

Apply log rule:

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

ln (2^{0.5}) - ln (1.10066) = ln (\frac{2 ^{0.5}}{1.10066})

= - \frac{364}{1740} - 1.144 + ln (\frac{2 ^{0.5}}{1.10066})

\frac{2 ^{0.5}}{1.10066} = 1.28487 \dots

= - \frac{364}{1740} - 1.144 + ln (1.28487 \dots)

Cancel

\frac{364}{1740} : \frac{91}{435}

= - \frac{91}{435} - 1.144 + ln (1.28487 \dots)

\frac{1}{2} \cdot ln (\frac{29}{5})

ln (\frac{2}{9}) - 4

ln (\frac{7.2 x}{1.66})

ln (49) - ln (9) - ln (4)

2 ln (3) - ln (4) - ln (2)

What is simplify-364/1740-1.144-ln(1.10066)+0.5ln(2) ?
The solution to simplify-364/1740-1.144-ln(1.10066)+0.5ln(2) is -91/435-1.144+ln(1.28487…)