What is 2ln(x)-3ln(y)+4ln(t) ?

The solution to 2ln(x)-3ln(y)+4ln(t) is ln((x^2t^4)/(y^3))

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simplify 2ln(x)-3ln(y)+4ln(t)

simplify

2 ln (x) - 3 ln (y) + 4 ln (t)

ln (\frac{x ^{2} t ^{4}}{y ^{3}})

Solution steps

2 ln (x) - 3 ln (y) + 4 ln (t)

Apply log rule:

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

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

= ln (x^{2}) - 3 ln (y) + 4 ln (t)

Apply log rule:

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

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

= ln (x^{2}) - ln (y^{3}) + 4 ln (t)

Apply log rule:

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

ln (x^{2}) - ln (y^{3}) = ln (\frac{x ^{2}}{y ^{3}})

= ln (\frac{x ^{2}}{y ^{3}}) + 4 ln (t)

Apply log rule:

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

4 ln (t) = ln (t^{4})

= ln (\frac{x ^{2}}{y ^{3}}) + ln (t^{4})

Apply log rule:

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

ln (\frac{x ^{2}}{y ^{3}}) + ln (t^{4}) = ln (\frac{x ^{2}}{y ^{3}} t^{4})

= ln (\frac{x ^{2}}{y ^{3}} t^{4})

Multiply fractions:

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

= ln (\frac{x ^{2} t ^{4}}{y ^{3}})

ln (\frac{e ^{6}}{11})

lo g_{10} (3) - lo g_{10} (11)

lo g_{10} (x^{2}) - lo g_{10} (x) y + 4 lo g_{10} (y)

lo g_{5} (x \cdot y \cdot z^{4})

lo g_{5} (x^{2} - 1) - lo g_{5} (x - 1)

What is 2ln(x)-3ln(y)+4ln(t) ?
The solution to 2ln(x)-3ln(y)+4ln(t) is ln((x^2t^4)/(y^3))