What is 1/3 (6ln(x+7)+ln(x)-ln(x^2-8)) ?

The solution to 1/3 (6ln(x+7)+ln(x)-ln(x^2-8)) is 1/3 ln(((x+7)^6x)/(x^2-8))

Popular >

simplify 1/3 (6ln(x+7)+ln(x)-ln(x^2-8))

simplify

\frac{1}{3} (6 ln (x + 7) + ln (x) - ln (x^{2} - 8))

\frac{1}{3} ln (\frac{( x + 7 ) ^{6} x}{x ^{2} - 8})

Solution steps

\frac{1}{3} (6 ln (x + 7) + ln (x) - ln (x^{2} - 8))

Apply log rule:

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

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

= \frac{1}{3} (ln ((x + 7)^{6}) + ln (x) - ln (x^{2} - 8))

Apply log rule:

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

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

= \frac{1}{3} (ln ((x + 7)^{6} x) - ln (x^{2} - 8))

Apply log rule:

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

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

= \frac{1}{3} ln (\frac{( x + 7 ) ^{6} x}{x ^{2} - 8})

- lo g_{10} (1.35 (1 0^{- 10}))

ln (1) + ln (3) - 2 ln (2)

ln (\frac{0.27}{2.21 \cdot 1 0 ^{4}}) \cdot \frac{8.314}{90315}

0.7 + 0.1 \cdot lo g_{10} (\frac{( 2.15 )}{15})

2 lo g_{8} (x) - \frac{1}{2} lo g_{8} (w) + 7 lo g_{8} (z)

What is 1/3 (6ln(x+7)+ln(x)-ln(x^2-8)) ?
The solution to 1/3 (6ln(x+7)+ln(x)-ln(x^2-8)) is 1/3 ln(((x+7)^6x)/(x^2-8))