What is ln(6)+ln(4)-ln(3) ?

The solution to ln(6)+ln(4)-ln(3) is 3ln(2)

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simplify ln(6)+ln(4)-ln(3)

simplify

ln (6) + ln (4) - ln (3)

3 ln (2)

Decimal Notation

2.07944 \dots

Solution steps

ln (6) + ln (4) - ln (3)

Apply log rule:

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

ln (6) + ln (4) = ln (6 \cdot 4)

= ln (6 \cdot 4) - ln (3)

Multiply the numbers:

6 \cdot 4 = 24

= ln (24) - ln (3)

Apply log rule:

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

ln (24) - ln (3) = ln (\frac{24}{3})

= ln (\frac{24}{3})

Divide the numbers:

\frac{24}{3} = 8

= ln (8)

Rewrite

8

in power-base form:

8 = 2^{3}

= ln (2^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 3 ln (2)

\frac{1}{2} lo g_{3} (x) - 4 lo g_{3} (y) - 2 lo g_{3} (z)

ln (\frac{6}{5 x ^{5} y})

lo g_{10} (79 x y)

lo g_{4} (8) + lo g_{4} (15) - lo g_{4} (14)

- lo g_{10} (5.6 \cdot 1 0^{- 6})