What is 3ln(x+8)-6ln(x^2+7) ?

The solution to 3ln(x+8)-6ln(x^2+7) is ln(((x+8)^3)/((x^2+7)^6))

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simplify 3ln(x+8)-6ln(x^2+7)

simplify

3 ln (x + 8) - 6 ln (x^{2} + 7)

ln (\frac{( x + 8 ) ^{3}}{( x ^{2} + 7 ) ^{6}})

Solution steps

3 ln (x + 8) - 6 ln (x^{2} + 7)

Apply log rule:

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

3 ln (x + 8) = ln ((x + 8)^{3})

= ln ((x + 8)^{3}) - 6 ln (x^{2} + 7)

Apply log rule:

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

6 ln (x^{2} + 7) = ln ((x^{2} + 7)^{6})

= ln ((x + 8)^{3}) - ln ((x^{2} + 7)^{6})

Apply log rule:

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

ln ((x + 8)^{3}) - ln ((x^{2} + 7)^{6}) = ln (\frac{( x + 8 ) ^{3}}{( x ^{2} + 7 ) ^{6}})

= ln (\frac{( x + 8 ) ^{3}}{( x ^{2} + 7 ) ^{6}})

lo g_{10} ((\frac{x ^{4}}{y})^{6})

4 \cdot lo g_{10} (x) - (2 \cdot lo g_{10} (v) + 3 \cdot lo g_{10} (y))

lo g_{10} (\frac{y z ^{4}}{x})

lo g_{10} (\frac{x + 1}{x ^{2} + 1})

lo g_{10} (x^{\frac{3}{5}} y^{4})

What is 3ln(x+8)-6ln(x^2+7) ?
The solution to 3ln(x+8)-6ln(x^2+7) is ln(((x+8)^3)/((x^2+7)^6))