What is 5ln(0.2+10)-5ln(10) ?

The solution to 5ln(0.2+10)-5ln(10) is ln(1.10408…)

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simplify 5ln(0.2+10)-5ln(10)

simplify

5 ln (0.2 + 10) - 5 ln (10)

ln (1.10408 \dots)

Decimal Notation

0.09901 \dots

Solution steps

5 ln (0.2 + 10) - 5 ln (10)

Apply log rule:

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

5 ln (10 + 0.2) = ln ((10 + 0.2)^{5})

= ln ((10 + 0.2)^{5}) - 5 ln (10)

Apply log rule:

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

5 ln (10) = ln (1 0^{5})

= ln ((10 + 0.2)^{5}) - ln (1 0^{5})

Apply log rule:

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

ln ((0.2 + 10)^{5}) - ln (1 0^{5}) = ln (\frac{( 10 + 0.2 ) ^{5}}{1 0 ^{5}})

= ln (\frac{( 0.2 + 10 ) ^{5}}{1 0 ^{5}})

\frac{( 0.2 + 10 ) ^{5}}{1 0 ^{5}} = 1.10408 \dots

= ln (1.10408 \dots)

ln (x) - [ln (x + 1) + ln (x - 1)]

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ln^{2} (\frac{a + a ^{2} + x ^{2}}{x})

\frac{1}{3} ln (8) + ln (3)

- 100 (ln ∣ 10 ∣ - ln ∣ 11 ∣) - 0.2321

What is 5ln(0.2+10)-5ln(10) ?
The solution to 5ln(0.2+10)-5ln(10) is ln(1.10408…)