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Popular >

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

Solution

simplify

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

Solution

ln (t u)

Solution steps

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

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 (u)

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 (u)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{t}{u ^{2}} u^{3} : t u

= ln (t u)

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Frequently Asked Questions (FAQ)

What is ln(t)-2ln(u)+3ln(u) ?
The solution to ln(t)-2ln(u)+3ln(u) is ln(tu)