What is 4ln(3)-5ln(z-6) ?

The solution to 4ln(3)-5ln(z-6) is ln((81)/((z-6)^5))

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simplify 4ln(3)-5ln(z-6)

simplify

4 ln (3) - 5 ln (z - 6)

ln (\frac{81}{( z - 6 ) ^{5}})

Solution steps

4 ln (3) - 5 ln (z - 6)

Apply log rule:

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

4 ln (3) = ln (3^{4})

= ln (3^{4}) - 5 ln (z - 6)

Apply log rule:

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

5 ln (z - 6) = ln ((z - 6)^{5})

= ln (3^{4}) - ln ((z - 6)^{5})

Apply log rule:

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

ln (3^{4}) - ln ((z - 6)^{5}) = ln (\frac{3 ^{4}}{( z - 6 ) ^{5}})

= ln (\frac{3 ^{4}}{( z - 6 ) ^{5}})

3^{4} = 81

= ln (\frac{81}{( z - 6 ) ^{5}})

3 \cdot lo g_{10} (a) - 2 \cdot lo g_{10} (b) - 1

(sin (x) - 1) (ln (sin (x)) - ln (cos (x)))

\frac{5}{9} lo g_{2} (3)

5 lo g_{7} (11) - lo g_{7} (3)

ln (956 \cdot 178108)