What is 2*ln(8)-2*ln(6) ?

The solution to 2*ln(8)-2*ln(6) is ln(16/9)

Popular >

simplify 2ln(8)-2ln(6)

simplify

2 \cdot ln (8) - 2 \cdot ln (6)

ln (\frac{16}{9})

Decimal

0.57536 \dots

Solution steps

2 ln (8) - 2 ln (6)

Apply log rule:

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

2 ln (8) = ln (8^{2})

= ln (8^{2}) - 2 ln (6)

Apply log rule:

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

2 ln (6) = ln (6^{2})

= ln (8^{2}) - ln (6^{2})

Apply log rule:

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

ln (8^{2}) - ln (6^{2}) = ln (\frac{8 ^{2}}{6 ^{2}})

= ln (\frac{8 ^{2}}{6 ^{2}})

\frac{8 ^{2}}{6 ^{2}} = \frac{16}{9}

= ln (\frac{16}{9})

10.64 + lo g_{10} (\frac{0.045072}{0.005616})

5 ln (2) + 3 ln (x) - \frac{1}{2} ln (x + 7)

ln (\frac{s ^{2}}{1 + s ^{2}})

lo g_{9} ((\frac{3 ^{3}}{7})^{4})

2 ln ∣ ln (x) ∣ + ln (x)