Write as a single logarithm and simplify.

Question

Write as a single logarithm and simplify. Do not evaluate with a calculator.

a. ) log(52x) – 2 log (2y) – log (4x)

b.) 4 ln 5 – ln 15 + ln 2

Answer 1

a) log(52x) – 2 log (2y) – log (4x)

log(52x) – log (2y)² – log (4x)

log (52x/(2y)²) - log (4x)

log (52x/4y²) - log (4x)

log(13x/y²) - log (4x)

log ((13x/y²)/4x)

log (13/4y²)

b.) 4 ln 5 – ln 15 + ln 2

ln 5⁴ - ln 15 + ln 2

ln (5⁴/15) + ln 2

ln (5³/3) + ln 2

ln (5³ 2/3)

ln 250/3