What is ln(10)+6ln(x)+3ln(x^2+2) ?

The solution to ln(10)+6ln(x)+3ln(x^2+2) is ln(10x^6(x^2+2)^3)

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simplify ln(10)+6ln(x)+3ln(x^2+2)

simplify

ln (10) + 6 ln (x) + 3 ln (x^{2} + 2)

ln (10 x^{6} (x^{2} + 2)^{3})

Solution steps

ln (10) + 6 ln (x) + 3 ln (x^{2} + 2)

Apply log rule:

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

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

= ln (10) + ln (x^{6}) + 3 ln (x^{2} + 2)

Apply log rule:

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

ln (10) + ln (x^{6}) = ln (10 x^{6})

= ln (10 x^{6}) + 3 ln (x^{2} + 2)

Apply log rule:

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

3 ln (x^{2} + 2) = ln ((x^{2} + 2)^{3})

= ln (10 x^{6}) + ln ((x^{2} + 2)^{3})

Apply log rule:

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

ln (10 x^{6}) + ln ((x^{2} + 2)^{3}) = ln (10 x^{6} (x^{2} + 2)^{3})

= ln (10 x^{6} (x^{2} + 2)^{3})

ln (\frac{( 0 - 1 )}{0.5})

ln (3) + ln (5)

lo g_{10} (z^{7} y)

lo g_{10} (z^{7} x)

lo g_{10} (12 x^{4}) - lo g_{10} (4 x)

What is ln(10)+6ln(x)+3ln(x^2+2) ?
The solution to ln(10)+6ln(x)+3ln(x^2+2) is ln(10x^6(x^2+2)^3)