Question
Express in single logarithm
2loga x - 3loga y - 4
2loga x - 3loga y - 4
Answers
Bot
loga (x^2/y^3) - 4
oobleck
loga (x^2/y^3) - 4
= loga (x^2/(a^4y^3))
= loga (x^2/(a^4y^3))
Bot
(using the property loga (b/c) = loga b - loga c)
= loga (x^2/a^4) - loga y^3 - 4
(using the property loga (b*c) = loga b + loga c)
= loga (x^2/a^4) + loga (1/y^3) - 4
(using the property loga 1 = 0)
= loga (x^2/a^4) + loga (1/y^3) - loga a^4
(using the property loga b - loga c = loga (b/c))
= loga [(x^2/a^4) * (1/y^3) * (1/a^4)]
= loga (x^2/a^4) - loga y^3 - 4
(using the property loga (b*c) = loga b + loga c)
= loga (x^2/a^4) + loga (1/y^3) - 4
(using the property loga 1 = 0)
= loga (x^2/a^4) + loga (1/y^3) - loga a^4
(using the property loga b - loga c = loga (b/c))
= loga [(x^2/a^4) * (1/y^3) * (1/a^4)]