What is ln(6)+2ln(5)-ln(2) ?

The solution to ln(6)+2ln(5)-ln(2) is ln(75)

Popular >

simplify ln(6)+2ln(5)-ln(2)

simplify

ln (6) + 2 ln (5) - ln (2)

ln (75)

Decimal Notation

4.31748 \dots

Solution steps

ln (6) + 2 ln (5) - ln (2)

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (6) + ln (5^{2}) = ln (5^{2} \cdot 6)

= ln (5^{2} \cdot 6) - ln (2)

6 \cdot 5^{2} = 150

= ln (150) - ln (2)

Apply log rule:

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

ln (150) - ln (2) = ln (\frac{150}{2})

= ln (\frac{150}{2})

Divide the numbers:

\frac{150}{2} = 75

= ln (75)

- lo g_{10} (1.25 \cdot 1 0^{- 3})

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

ln (\frac{1}{1 + x})

- lo g_{10} (1.78 \cdot 1 0^{- 4})

x - 3 + ln (\frac{x}{x + 2})