What is simplify-ln(2)+ln(10)-2ln(3) ?

The solution to simplify-ln(2)+ln(10)-2ln(3) is ln(5/9)

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simplify-ln(2)+ln(10)-2ln(3)

simplify

- ln (2) + ln (10) - 2 ln (3)

ln (\frac{5}{9})

Decimal Notation

- 0.58778 \dots

Solution steps

- ln (2) + ln (10) - 2 ln (3)

Apply log rule:

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

ln (10) - ln (2) = ln (\frac{10}{2})

= ln (\frac{10}{2}) - 2 ln (3)

Divide the numbers:

\frac{10}{2} = 5

= ln (5) - 2 ln (3)

Apply log rule:

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

2 ln (3) = ln (3^{2})

= ln (5) - ln (3^{2})

Apply log rule:

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

ln (5) - ln (3^{2}) = ln (\frac{5}{3 ^{2}})

= ln (\frac{5}{3 ^{2}})

3^{2} = 9

= ln (\frac{5}{9})

7 ln (x) - ln (x^{2} - 25)

- lo g_{10} (2.62 \cdot 1 0^{- 6})

- lo g_{10} (1.89 (1 0^{- 3}))

ln (x^{2} e^{3})

What is simplify-ln(2)+ln(10)-2ln(3) ?
The solution to simplify-ln(2)+ln(10)-2ln(3) is ln(5/9)