What is 2*ln(7)-6*ln(z-9) ?

The solution to 2*ln(7)-6*ln(z-9) is ln((49)/((z-9)^6))

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simplify 2ln(7)-6ln(z-9)

simplify

2 \cdot ln (7) - 6 \cdot ln (z - 9)

ln (\frac{49}{( z - 9 ) ^{6}})

Solution steps

2 ln (7) - 6 ln (z - 9)

Apply log rule:

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

2 ln (7) = ln (7^{2})

= ln (7^{2}) - 6 ln (z - 9)

Apply log rule:

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

6 ln (z - 9) = ln ((z - 9)^{6})

= ln (7^{2}) - ln ((z - 9)^{6})

Apply log rule:

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

ln (7^{2}) - ln ((z - 9)^{6}) = ln (\frac{7 ^{2}}{( z - 9 ) ^{6}})

= ln (\frac{7 ^{2}}{( z - 9 ) ^{6}})

7^{2} = 49

= ln (\frac{49}{( z - 9 ) ^{6}})

\frac{63}{17} ln ∣ - 4 ∣ - \frac{63}{17} ln ∣ - 8 ∣

lo g_{8} (3 x^{3})

lo g_{\frac{1}{2}} (\frac{1}{2000})

\frac{π}{8} (ln (13) - ln (5))

ln (\frac{29000}{24000})

What is 2*ln(7)-6*ln(z-9) ?
The solution to 2*ln(7)-6*ln(z-9) is ln((49)/((z-9)^6))