What is ln(10)+ln(10)-ln(5)-ln(15) ?

The solution to ln(10)+ln(10)-ln(5)-ln(15) is ln(4/3)

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simplify ln(10)+ln(10)-ln(5)-ln(15)

simplify

ln (10) + ln (10) - ln (5) - ln (15)

ln (\frac{4}{3})

Decimal Notation

0.28768 \dots

Solution steps

ln (10) + ln (10) - ln (5) - ln (15)

Apply log rule:

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

ln (10) - ln (5) = ln (\frac{10}{5})

= ln (10) + ln (\frac{10}{5}) - ln (15)

Divide the numbers:

\frac{10}{5} = 2

= ln (10) + ln (2) - ln (15)

Apply log rule:

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

ln (10) + ln (2) = ln (10 \cdot 2)

= ln (10 \cdot 2) - ln (15)

Multiply the numbers:

10 \cdot 2 = 20

= ln (20) - ln (15)

Apply log rule:

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

ln (20) - ln (15) = ln (\frac{20}{15})

= ln (\frac{20}{15})

Cancel the common factor:

5

= ln (\frac{4}{3})

- lo g_{10} (3.16 \cdot 1 0^{2})

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

- lo g_{10} (1.15 \cdot 1 0^{- 15})

ln (\frac{e + 1}{2})

lo g_{5} (7 x)

What is ln(10)+ln(10)-ln(5)-ln(15) ?
The solution to ln(10)+ln(10)-ln(5)-ln(15) is ln(4/3)