Question

Write as a sum or difference of logarithms with no unnecesssry exponents left.
ln ((5x^4)(2x-1)^7) / (([square root] x^2 +1)(3x+2)^19)

Answer 1

\[\ln 5x^4 (2x-1)^7 \div \sqrt{x^2 +1}(3x+2)^19\]

Answer 2

except the last exponent is 19

Answer 3

for the numerator you will need to apply these rules.

\[\log(ab) = \log(a) + \log(b)\]

and the index rule is

\[\log(x^a) = a \times \log(x)..... or....alog(x)\]

for the denominator

\[\sqrt{(x^2 +1)(3x + 2)^19} = \sqrt{(x^2 +1) \times (3x + 2)^{18} \times (3x + 2)} = \sqrt{(3x +2)^{18}} \times \sqrt{(x^2 +1)(3x + 2)}\]

you need to finish simplifying the denominator