What is 4ln(x+6/4)+ln(x+1) ?

The solution to 4ln(x+6/4)+ln(x+1) is ln((x+3/2)^4(x+1))

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simplify 4ln(x+6/4)+ln(x+1)

simplify

4 ln (x + \frac{6}{4}) + ln (x + 1)

ln ((x + \frac{3}{2})^{4} (x + 1))

Solution steps

4 ln (x + \frac{6}{4}) + ln (x + 1)

Apply log rule:

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

4 ln (x + \frac{6}{4}) = ln ((x + \frac{6}{4})^{4})

= ln ((x + \frac{6}{4})^{4}) + ln (x + 1)

Apply log rule:

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

ln ((x + \frac{6}{4})^{4}) + ln (x + 1) = ln ((x + 1) (x + \frac{6}{4})^{4})

= ln ((x + \frac{6}{4})^{4} (x + 1))

(x + \frac{6}{4})^{4} = (x + \frac{3}{2})^{4}

= ln ((x + \frac{3}{2})^{4} (x + 1))

ln (10 x) - ln (z)

lo g_{9} ((x y^{3})^{3})

What is 4ln(x+6/4)+ln(x+1) ?
The solution to 4ln(x+6/4)+ln(x+1) is ln((x+3/2)^4(x+1))