What is ln(x)-ln(y)+ln(z)+ln(3) ?

The solution to ln(x)-ln(y)+ln(z)+ln(3) is ln((3xz)/y)

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simplify ln(x)-ln(y)+ln(z)+ln(3)

simplify

ln (x) - ln (y) + ln (z) + ln (3)

ln (\frac{3 x z}{y})

Solution steps

ln (x) - ln (y) + ln (z) + ln (3)

Apply log rule:

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

ln (x) - ln (y) = ln (\frac{x}{y})

= ln (\frac{x}{y}) + ln (z) + ln (3)

Apply log rule:

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

ln (\frac{x}{y}) + ln (z) = ln (\frac{x}{y} z)

= ln (\frac{x}{y} z) + ln (3)

Multiply fractions:

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

= ln (\frac{x z}{y}) + ln (3)

Apply log rule:

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

ln (\frac{x z}{y}) + ln (3) = ln (3 \cdot \frac{x z}{y})

= ln (3 \cdot \frac{x z}{y})

Multiply fractions:

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

= ln (\frac{3 x z}{y})

- ln (\frac{y}{x})

ln (\frac{5 - 4 x}{x + 2})

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ln (\frac{1}{125}) + 4 ln (5) - 2 ln (\frac{1}{5})

What is ln(x)-ln(y)+ln(z)+ln(3) ?
The solution to ln(x)-ln(y)+ln(z)+ln(3) is ln((3xz)/y)