What is ln(48)-ln(15)-ln(7)+ln(4) ?

The solution to ln(48)-ln(15)-ln(7)+ln(4) is ln(64/35)

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simplify ln(48)-ln(15)-ln(7)+ln(4)

simplify

ln (48) - ln (15) - ln (7) + ln (4)

ln (\frac{64}{35})

Decimal Notation

0.60353 \dots

Solution steps

ln (48) - ln (15) - ln (7) + ln (4)

Apply log rule:

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

ln (48) - ln (15) = ln (\frac{48}{15})

= ln (\frac{48}{15}) - ln (7) + ln (4)

Cancel the common factor:

3

= ln (\frac{16}{5}) - ln (7) + ln (4)

Apply log rule:

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

ln (\frac{16}{5}) - ln (7) = ln (\frac{\frac{16}{5}}{7})

= ln (\frac{\frac{16}{5}}{7}) + ln (4)

\frac{\frac{16}{5}}{7} = \frac{16}{35}

= ln (\frac{16}{35}) + ln (4)

Apply log rule:

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

ln (\frac{16}{35}) + ln (4) = ln (4 \cdot \frac{16}{35})

= ln (4 \cdot \frac{16}{35})

\frac{16}{35} \cdot 4 = \frac{64}{35}

= ln (\frac{64}{35})

ln (\frac{1.36}{12})

ln (2 (e^{x} + 1)^{2}) + ln (c)

ln (6 (1 - e^{- 5}))

+ \frac{1}{3} ln (3312)

ln (6) - ln (3)

What is ln(48)-ln(15)-ln(7)+ln(4) ?
The solution to ln(48)-ln(15)-ln(7)+ln(4) is ln(64/35)