What is ln(ln(5)-7ln(10)) ?

The solution to ln(ln(5)-7ln(10)) is ln(-ln(2000000))

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simplify ln(ln(5)-7ln(10))

simplify

ln (ln (5) - 7 ln (10))

ln (- ln (2000000))

Solution steps

ln (ln (5) - 7 ln (10))

Apply log rule:

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

7 ln (10) = ln (1 0^{7})

= ln (ln (5) - ln (1 0^{7}))

Apply log rule:

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

ln (5) - ln (1 0^{7}) = ln (\frac{5}{1 0 ^{7}})

= ln (ln (\frac{5}{1 0 ^{7}}))

\frac{5}{1 0 ^{7}} = \frac{1}{2000000}

= ln (ln (\frac{1}{2000000}))

Simplify

ln (\frac{1}{2000000}) : - ln (2000000)

= ln (- ln (2000000))

ln (\frac{2000}{1999}) 111

- 0.402 - \frac{0.05916}{2} lo g_{10} (\frac{0.5}{1})

4.184 \cdot ln (\frac{( 273.15 + 60 )}{( 273.15 + 18 )})

ln (x) + 6 ln (\frac{y + x}{x}) - 9 ln (\frac{y + 2 x}{x})

- 7 ln (7 \cdot 0.9)

What is ln(ln(5)-7ln(10)) ?
The solution to ln(ln(5)-7ln(10)) is ln(-ln(2000000))