What is 5ln(x-8)-4ln(x) ?

The solution to 5ln(x-8)-4ln(x) is ln(((x-8)^5)/(x^4))

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simplify 5ln(x-8)-4ln(x)

simplify

5 ln (x - 8) - 4 ln (x)

ln (\frac{( x - 8 ) ^{5}}{x ^{4}})

Solution steps

5 ln (x - 8) - 4 ln (x)

Apply log rule:

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

5 ln (x - 8) = ln ((x - 8)^{5})

= ln ((x - 8)^{5}) - 4 ln (x)

Apply log rule:

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

4 ln (x) = ln (x^{4})

= ln ((x - 8)^{5}) - ln (x^{4})

Apply log rule:

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

ln ((x - 8)^{5}) - ln (x^{4}) = ln (\frac{( x - 8 ) ^{5}}{x ^{4}})

= ln (\frac{( x - 8 ) ^{5}}{x ^{4}})

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{3}})

\frac{1}{3} (ln (x) + ln (x - 6) - ln (x^{3} + 9))

\frac{1}{2} lo g_{10} (x + 3) + \frac{1}{2} lo g_{10} (2 x - 1)

\frac{ln ( \frac{69}{97} )}{2 ln ( 2 )}

\frac{1}{5} lo g_{3} (10)

What is 5ln(x-8)-4ln(x) ?
The solution to 5ln(x-8)-4ln(x) is ln(((x-8)^5)/(x^4))