What is 1/2 [5ln(x+1)+ln(x)-ln(x^5-3)] ?

The solution to 1/2 [5ln(x+1)+ln(x)-ln(x^5-3)] is 1/2 ln((x(x+1)^5)/(x^5-3))

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simplify 1/2 [5ln(x+1)+ln(x)-ln(x^5-3)]

simplify

\frac{1}{2} [5 ln (x + 1) + ln (x) - ln (x^{5} - 3)]

\frac{1}{2} ln (\frac{x ( x + 1 ) ^{5}}{x ^{5} - 3})

Solution steps

\frac{1}{2} [5 ln (x + 1) + ln (x) - ln (x^{5} - 3)]

Apply log rule:

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

5 ln (x + 1) = ln ((x + 1)^{5})

= \frac{1}{2} [ln ((x + 1)^{5}) + ln (x) - ln (x^{5} - 3)]

Apply log rule:

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

ln ((x + 1)^{5}) + ln (x) = ln (x (x + 1)^{5})

= \frac{1}{2} [ln ((x + 1)^{5} x) - ln (x^{5} - 3)]

Apply log rule:

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

ln (x (x + 1)^{5}) - ln (x^{5} - 3) = ln (\frac{x ( x + 1 ) ^{5}}{x ^{5} - 3})

= \frac{1}{2} [ln (\frac{( x + 1 ) ^{5} x}{x ^{5} - 3})]

Remove parentheses:

(a) = a

= \frac{1}{2} ln (\frac{( x + 1 ) ^{5} x}{x ^{5} - 3})

- lo g_{10} (1.8 \cdot 1 0^{- 9})

- lo g_{10} (5.29 \cdot 1 0^{- 6})

- lo g_{10} (4.2 \cdot 1 0^{- 5})

lo g_{10} (1000 y)

What is 1/2 [5ln(x+1)+ln(x)-ln(x^5-3)] ?
The solution to 1/2 [5ln(x+1)+ln(x)-ln(x^5-3)] is 1/2 ln((x(x+1)^5)/(x^5-3))