What is 2.6-200ln(103)+0.15ln(110) ?

The solution to 2.6-200ln(103)+0.15ln(110) is 2.6+200ln((2.02399…)/(103^{200)})

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simplify 2.6-200ln(103)+0.15ln(110)

simplify

2.6 - 200 ln (103) + 0.15 ln (110)

2.6 + 200 ln (\frac{2.02399 \dots}{10 3 ^{200}})

Solution steps

2.6 - 200 ln (103) + 0.15 ln (110)

Apply log rule:

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

0.15 ln (110) = ln (11 0^{0.15})

= 2.6 - 200 ln (103) + ln (11 0^{0.15})

Apply log rule:

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

ln (11 0^{0.15}) - ln (103) = ln (\frac{11 0 ^{0.15}}{103})

= 2.6 + 200 ln (\frac{11 0 ^{0.15}}{103})

11 0^{0.15} = 2.02399 \dots

= 2.6 + 200 ln (\frac{2.02399 \dots}{10 3 ^{200}})

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What is 2.6-200ln(103)+0.15ln(110) ?
The solution to 2.6-200ln(103)+0.15ln(110) is 2.6+200ln((2.02399…)/(103^{200)})