Question

Express the following as a single logarithm:
log 144 - log 72 + log 150 - log 50

Answer 1

log 144 - log 72 + log 150 - log 50
= log (2⁴ x 3²) - log (2³ x 3²) + log (2 x 3 x 5²) - log (2 x 5²)
= log 2⁴ + log 3² - {log 2³ + log 3²} + log 2 + log 3 + 5² - {log 2 + log 5²}
= 4 log 2 + 2 log 3 - 3 log 2 - 2 log 3 + log 2 + log 3 + 2 log 5 - log 2 - 2 log 5
= log 2 + log 3
= log (2 x 3)
= log 6.