What is 5ln(x^3)-2ln(x^4) ?

The solution to 5ln(x^3)-2ln(x^4) is ln(x^7)

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simplify 5ln(x^3)-2ln(x^4)

simplify

5 ln (x^{3}) - 2 ln (x^{4})

ln (x^{7})

Solution steps

5 ln (x^{3}) - 2 ln (x^{4})

Apply log rule:

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

5 ln (x^{3}) = ln ((x^{3})^{5})

= ln ((x^{3})^{5}) - 2 ln (x^{4})

Apply log rule:

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

2 ln (x^{4}) = ln ((x^{4})^{2})

= ln ((x^{3})^{5}) - ln ((x^{4})^{2})

Apply log rule:

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

ln ((x^{3})^{5}) - ln ((x^{4})^{2}) = ln (\frac{( x ^{3} ) ^{5}}{( x ^{4} ) ^{2}})

= ln (\frac{( x ^{3} ) ^{5}}{( x ^{4} ) ^{2}})

Simplify

\frac{( x ^{3} ) ^{5}}{( x ^{4} ) ^{2}} : x^{7}

= ln (x^{7})

\frac{1}{4} lo g_{c} (x) + 2 lo g_{c} (y) - 4 lo g_{c} (x)

lo g_{4} (\frac{1}{16} x)

2 lo g_{10} (a) + 3 lo g_{10} (b)

lo g_{8} (x z^{3})

lo g_{10} (z) - lo g_{10} (13)