What is 5-2ln(6.7)+ln(5.7) ?

The solution to 5-2ln(6.7)+ln(5.7) is 5+ln(0.12697…)

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simplify 5-2ln(6.7)+ln(5.7)

simplify

5 - 2 ln (6.7) + ln (5.7)

5 + ln (0.12697 \dots)

Decimal Notation

2.93625 \dots

Solution steps

5 - 2 ln (6.7) + ln (5.7)

Apply log rule:

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

2 ln (6.7) = ln (6. 7^{2})

= 5 - ln (6. 7^{2}) + ln (5.7)

Apply log rule:

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

ln (5.7) - ln (6. 7^{2}) = ln (\frac{5.7}{6. 7 ^{2}})

= 5 + ln (\frac{5.7}{6. 7 ^{2}})

\frac{5.7}{6. 7 ^{2}} = 0.12697 \dots

= 5 + ln (0.12697 \dots)

\frac{57}{40} + \frac{4}{5} ln (\frac{5}{4}) - \frac{3}{8} ln (2)

4 + 2 ln (\frac{2 + 1}{2 - 1})

d + θ ln (k) + γ ln (ω) - ln (\frac{1}{1 + βθ} k^{α} ω) - β d

6 lo g_{8} (u) + 6 lo g_{8} (w) - 36 lo g_{8} (v)

- lo g_{10} (5 \cdot 1 0^{8})

What is 5-2ln(6.7)+ln(5.7) ?
The solution to 5-2ln(6.7)+ln(5.7) is 5+ln(0.12697…)