What is 7ln(t)-6ln(s)+5ln(w) ?

The solution to 7ln(t)-6ln(s)+5ln(w) is ln((t^7w^5)/(s^6))

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simplify 7ln(t)-6ln(s)+5ln(w)

simplify

7 ln (t) - 6 ln (s) + 5 ln (w)

ln (\frac{t ^{7} w ^{5}}{s ^{6}})

Solution steps

7 ln (t) - 6 ln (s) + 5 ln (w)

Apply log rule:

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

7 ln (t) = ln (t^{7})

= ln (t^{7}) - 6 ln (s) + 5 ln (w)

Apply log rule:

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

6 ln (s) = ln (s^{6})

= ln (t^{7}) - ln (s^{6}) + 5 ln (w)

Apply log rule:

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

ln (t^{7}) - ln (s^{6}) = ln (\frac{t ^{7}}{s ^{6}})

= ln (\frac{t ^{7}}{s ^{6}}) + 5 ln (w)

Apply log rule:

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

5 ln (w) = ln (w^{5})

= ln (\frac{t ^{7}}{s ^{6}}) + ln (w^{5})

Apply log rule:

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

ln (\frac{t ^{7}}{s ^{6}}) + ln (w^{5}) = ln (\frac{t ^{7}}{s ^{6}} w^{5})

= ln (\frac{t ^{7}}{s ^{6}} w^{5})

Multiply fractions:

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

= ln (\frac{t ^{7} w ^{5}}{s ^{6}})

ln (\frac{a}{b ^{3}})

lo g_{10} (\frac{π}{2})

ln (\frac{( w ^{3} )}{z})

ln (2 x) - 2 ln (y) + ln (z)

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

What is 7ln(t)-6ln(s)+5ln(w) ?
The solution to 7ln(t)-6ln(s)+5ln(w) is ln((t^7w^5)/(s^6))