What is 1/3 (6ln(x+5)+ln(x)-ln(x^2-6)) ?

The solution to 1/3 (6ln(x+5)+ln(x)-ln(x^2-6)) is 1/3 ln(((x+5)^6x)/(x^2-6))

Popular >

simplify 1/3 (6ln(x+5)+ln(x)-ln(x^2-6))

simplify

\frac{1}{3} (6 ln (x + 5) + ln (x) - ln (x^{2} - 6))

\frac{1}{3} ln (\frac{( x + 5 ) ^{6} x}{x ^{2} - 6})

Solution steps

\frac{1}{3} (6 ln (x + 5) + ln (x) - ln (x^{2} - 6))

Apply log rule:

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

6 ln (x + 5) = ln ((x + 5)^{6})

= \frac{1}{3} (ln ((x + 5)^{6}) + ln (x) - ln (x^{2} - 6))

Apply log rule:

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

ln ((x + 5)^{6}) + ln (x) = ln (x (x + 5)^{6})

= \frac{1}{3} (ln ((x + 5)^{6} x) - ln (x^{2} - 6))

Apply log rule:

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

ln (x (x + 5)^{6}) - ln (x^{2} - 6) = ln (\frac{x ( x + 5 ) ^{6}}{x ^{2} - 6})

= \frac{1}{3} ln (\frac{( x + 5 ) ^{6} x}{x ^{2} - 6})

1.464 - lo g_{10} (\frac{1}{1 0 ^{0.3}})

\frac{( ln ( 2 ) \cdot 45 )}{ln ( 10 ) - ln ( 2 )}

- 20 lo g_{10} (0.2 1 - 0.01)

lo g_{10} (\frac{4 p ^{3}}{5 q ^{4}})

ln \frac{7}{5} + \frac{3}{4} x - ln - \frac{3}{5} + \frac{3}{5} x

What is 1/3 (6ln(x+5)+ln(x)-ln(x^2-6)) ?
The solution to 1/3 (6ln(x+5)+ln(x)-ln(x^2-6)) is 1/3 ln(((x+5)^6x)/(x^2-6))