What is ln(8)+ln(10)-ln(14)-ln(4) ?

The solution to ln(8)+ln(10)-ln(14)-ln(4) is ln(10/7)

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simplify ln(8)+ln(10)-ln(14)-ln(4)

simplify

ln (8) + ln (10) - ln (14) - ln (4)

ln (\frac{10}{7})

Decimal Notation

0.35667 \dots

Solution steps

ln (8) + ln (10) - ln (14) - ln (4)

Apply log rule:

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

ln (8) + ln (10) = ln (8 \cdot 10)

= ln (8 \cdot 10) - ln (14) - ln (4)

Multiply the numbers:

8 \cdot 10 = 80

= ln (80) - ln (14) - ln (4)

Apply log rule:

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

ln (80) - ln (14) = ln (\frac{80}{14})

= ln (\frac{80}{14}) - ln (4)

Cancel the common factor:

2

= ln (\frac{40}{7}) - ln (4)

Apply log rule:

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

ln (\frac{40}{7}) - ln (4) = ln (\frac{\frac{40}{7}}{4})

= ln (\frac{\frac{40}{7}}{4})

\frac{\frac{40}{7}}{4} = \frac{10}{7}

= ln (\frac{10}{7})

ln (\frac{20}{5})

0.026 ln (0.095 \cdot 1 0^{16})

lo g_{2} (- x) + lo g_{2} (1 - x) - 1

\frac{1}{3} (ln (y) - 2 ln (z) + 3 ln (x))

lo g_{e} (\frac{5}{3}) \cdot 100

What is ln(8)+ln(10)-ln(14)-ln(4) ?
The solution to ln(8)+ln(10)-ln(14)-ln(4) is ln(10/7)