What is simplify-ln(8)+ln(6)+ln(3)-ln(1) ?

The solution to simplify-ln(8)+ln(6)+ln(3)-ln(1) is ln(9/4)

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simplify-ln(8)+ln(6)+ln(3)-ln(1)

simplify

- ln (8) + ln (6) + ln (3) - ln (1)

ln (\frac{9}{4})

Solution steps

- ln (8) + ln (6) + ln (3) - ln (1)

Apply log rule:

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

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

= ln (\frac{6}{8}) + ln (3) - ln (1)

Cancel the common factor:

2

= ln (\frac{3}{4}) + ln (3) - ln (1)

Apply log rule:

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

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

= ln (3 \cdot \frac{3}{4}) - ln (1)

\frac{3}{4} \cdot 3 = \frac{9}{4}

= ln (\frac{9}{4}) - ln (1)

Apply log rule:

lo g_{a} (1) = 0

= ln (\frac{9}{4}) - 0

ln (\frac{9}{4}) - 0 = ln (\frac{9}{4})

= ln (\frac{9}{4})

lo g_{10} (1 0^{x})

- ln (5 \cdot 2) + 1

ln (\frac{2 + h}{2})

\frac{1}{3} ln (\frac{50}{60})

- \frac{1}{30} ln (\frac{8}{15})

What is simplify-ln(8)+ln(6)+ln(3)-ln(1) ?
The solution to simplify-ln(8)+ln(6)+ln(3)-ln(1) is ln(9/4)