What is ln(5)+ln(7)-3ln(2) ?

The solution to ln(5)+ln(7)-3ln(2) is ln(35/8)

Popular >

simplify ln(5)+ln(7)-3ln(2)

simplify

ln (5) + ln (7) - 3 ln (2)

ln (\frac{35}{8})

Decimal Notation

1.47590 \dots

Solution steps

ln (5) + ln (7) - 3 ln (2)

Apply log rule:

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

ln (5) + ln (7) = ln (5 \cdot 7)

= ln (5 \cdot 7) - 3 ln (2)

Multiply the numbers:

5 \cdot 7 = 35

= ln (35) - 3 ln (2)

Apply log rule:

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

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

= ln (35) - ln (2^{3})

Apply log rule:

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

ln (35) - ln (2^{3}) = ln (\frac{35}{2 ^{3}})

= ln (\frac{35}{2 ^{3}})

2^{3} = 8

= ln (\frac{35}{8})

ln (5 e^{3})

- lo g_{10} (2.3 \cdot 1 0^{- 7})

ln (\frac{x ^{8} x ^{2} + 2}{( x + 2 ) ^{9}})

- lo g_{10} (8.4 \cdot 1 0^{- 11})

ln \frac{x + 5}{2} + 1 - ln \frac{x + 5}{2} - 1