What is ln(t)-2ln(u)+3ln(v) ?

The solution to ln(t)-2ln(u)+3ln(v) is ln((tv^3)/(u^2))

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simplify ln(t)-2ln(u)+3ln(v)

simplify

ln (t) - 2 ln (u) + 3 ln (v)

ln (\frac{t v ^{3}}{u ^{2}})

Solution steps

ln (t) - 2 ln (u) + 3 ln (v)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (u) = ln (u^{2})

= ln (t) - ln (u^{2}) + 3 ln (v)

Apply log rule:

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

ln (t) - ln (u^{2}) = ln (\frac{t}{u ^{2}})

= ln (\frac{t}{u ^{2}}) + 3 ln (v)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (v) = ln (v^{3})

= ln (\frac{t}{u ^{2}}) + ln (v^{3})

Apply log rule:

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

ln (\frac{t}{u ^{2}}) + ln (v^{3}) = ln (\frac{t}{u ^{2}} v^{3})

= ln (\frac{t}{u ^{2}} v^{3})

Multiply fractions:

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

= ln (\frac{t v ^{3}}{u ^{2}})

3 lo g_{9} (x) - 18 lo g_{9} (y)

ln (\frac{5 x}{y ^{2}})

\frac{1}{3} ln (\frac{1}{27})

ln (3 x) + 1

lo g_{e} (22)

What is ln(t)-2ln(u)+3ln(v) ?
The solution to ln(t)-2ln(u)+3ln(v) is ln((tv^3)/(u^2))