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

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

Popular >

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} (\frac{a}{b})

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

= ln (6) + + ln (\frac{4}{3})

Apply log rule:

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

ln (6) + ln (\frac{4}{3}) = ln (6 \cdot \frac{4}{3})

= ln (6 \cdot \frac{4}{3})

6 \cdot \frac{4}{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_{b} (x) + 5 lo g_{b} (y) - 2 lo g_{b} (x)

lo g_{10} (3) + lo g_{10} (x)

lo g_{3} (\frac{x y ^{2}}{z ^{2}})

lo g_{10} (20) + lo g_{10} (4)

lo g_{2} (\frac{x + 3}{x y})