What is 4(ln(z)+ln(z+5)-2ln(z-5)) ?

The solution to 4(ln(z)+ln(z+5)-2ln(z-5)) is 4ln((z(z+5))/((z-5)^2))

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simplify 4(ln(z)+ln(z+5)-2ln(z-5))

simplify

4 (ln (z) + ln (z + 5) - 2 ln (z - 5))

4 ln (\frac{z ( z + 5 )}{( z - 5 ) ^{2}})

Solution steps

4 (ln (z) + ln (z + 5) - 2 ln (z - 5))

Apply log rule:

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

ln (z) + ln (z + 5) = ln (z (z + 5))

= 4 (ln (z (z + 5)) - 2 ln (z - 5))

Apply log rule:

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

2 ln (z - 5) = ln ((z - 5)^{2})

= 4 (ln (z (z + 5)) - ln ((z - 5)^{2}))

Apply log rule:

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

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

= 4 ln (\frac{z ( z + 5 )}{( z - 5 ) ^{2}})

ln (x + 3) ln (y) - ln (x y)

ln (y^{2} + 2) - ln (y^{2} - 5)

- lo g_{10} (6.3 \cdot 1 0^{- 2})

ln (x) - ln (x + 2)

ln ((2 x + 1)^{5} (x^{4} - 3)^{6})

What is 4(ln(z)+ln(z+5)-2ln(z-5)) ?
The solution to 4(ln(z)+ln(z+5)-2ln(z-5)) is 4ln((z(z+5))/((z-5)^2))