What is ln(x)-ln(v)+ln(v^2+12) ?

The solution to ln(x)-ln(v)+ln(v^2+12) is ln((x(v^2+12))/v)

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simplify ln(x)-ln(v)+ln(v^2+12)

simplify

ln (x) - ln (v) + ln (v^{2} + 12)

ln (\frac{x ( v ^{2} + 12 )}{v})

Solution steps

ln (x) - ln (v) + ln (v^{2} + 12)

Apply log rule:

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

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

= ln (\frac{x}{v}) + ln (v^{2} + 12)

Apply log rule:

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

ln (\frac{x}{v}) + ln (v^{2} + 12) = ln (\frac{x}{v} (v^{2} + 12))

= ln (\frac{x}{v} (v^{2} + 12))

Multiply fractions:

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

= ln (\frac{x ( v ^{2} + 12 )}{v})

\frac{43 π}{10} + ln (7) - \frac{1}{2} \cdot ln (26) - 169760

ln (\frac{2 x}{e ^{2 x}})

\frac{1}{2} ln (x - 3) + \frac{1}{2} ln (x + 3) - ln (x)

4.74 + lo g_{10} (\frac{50}{10})

What is ln(x)-ln(v)+ln(v^2+12) ?
The solution to ln(x)-ln(v)+ln(v^2+12) is ln((x(v^2+12))/v)