Question

Write as a single logarithm

Answer 1

ANSWER

$c. \ln( \frac{2 {x}^{3} }{3y})$

EXPLANATION

We want to write

$ln(2x) + 2 ln(x) - ln(3y)$

as a single logarithm.

Use the power rule to rewrite the middle term:

$n \: ln(a) = ln( {a}^{n} )$

$ln(2x) + ln( {x}^{2} ) - ln(3y)$

Use the product rule to obtain:

$ln(a) + ln(b) = ln(ab)$

$ln(2x \times {x}^{2} )- ln(3y)$

$ln(2{x}^{3} )- ln(3y)$

Apply the quotient rule:

$ln(a) - ln(b) = ln( \frac{a}{b})$

$ln(2{x}^{3} )- ln(3y) =\ln(\frac{2 {x}^{3} }{3y})$