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

The solution to ln(a)+ln(b)-(ln(a)+ln(c)) is ln(b/c)

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

simplify

ln (a) + ln (b) - (ln (a) + ln (c))

ln (\frac{b}{c})

Solution steps

ln (a) + ln (b) - (ln (a) + ln (c))

Apply log rule:

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

ln (a) + ln (b) = ln (ab)

= ln (ab) - (ln (a) + ln (c))

Apply log rule:

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

ln (a) + ln (c) = ln (a c)

= ln (ab) - ln (a c)

Apply log rule:

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

ln (ab) - ln (a c) = ln (\frac{ab}{a c})

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

Cancel the common factor:

a

= ln (\frac{b}{c})

2 ln (5) - ln (2)

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ln (e (x + 3))

- 9711 \cdot ln (\frac{10}{100})

ln (5 e^{x})

What is ln(a)+ln(b)-(ln(a)+ln(c)) ?
The solution to ln(a)+ln(b)-(ln(a)+ln(c)) is ln(b/c)