What is ln(d)-ln(a*b)+ln(c) ?

The solution to ln(d)-ln(a*b)+ln(c) is ln((dc)/(ab))

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simplify ln(d)-ln(a*b)+ln(c)

simplify

ln (d) - ln (a \cdot b) + ln (c)

ln (\frac{d c}{ab})

Solution steps

ln (d) - ln (ab) + ln (c)

Apply log rule:

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

ln (d) - ln (ab) = ln (\frac{d}{ab})

= ln (\frac{d}{ab}) + ln (c)

Apply log rule:

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

ln (\frac{d}{ab}) + ln (c) = ln (c \frac{d}{ab})

= ln (c \frac{d}{ab})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{d c}{ab})

6 lo g_{7} (7 x + 1) + \frac{1}{4} lo g_{7} (x + 4)

- lo g_{10} (4.55 \cdot 1 0^{- 8})

- \frac{1}{6} \cdot lo g_{2} (\frac{1}{6}) - \frac{5}{6} \cdot lo g_{2} (\frac{5}{6})

5 ln (x + 4) - 8 ln (x)

\frac{1}{3} (ln (x) + ln (y)) - 4 ln (z)

What is ln(d)-ln(a*b)+ln(c) ?
The solution to ln(d)-ln(a*b)+ln(c) is ln((dc)/(ab))