Question 1154: What is the single logarithm of ln 5 +2ln x-3ln(x2+1)?
What is the single logarithm of 2log5x+3log5y-4log5z Answer by khwang(438) (Show Source):
You can put this solution on YOUR website! Use n loga b = loga b^n
ln 5 + 2ln x-3ln(x2+1)
= ln 5 + ln x^2 + ln (x^2+1)^(-3)
then use loga x +loga y = loga x*y
= ln [5 * x^2 *(x^2+1)^(-3)]
= ln [5 x^2 /(x^2+1)^3] (negative exponent)
Similarly:
2log5x+3log5y-4log5z
= log5 x^2 + log5 y^3 + log5 z^(-4)
= log5 [x^2 * y^3 * z^(-4)]
= log5 [x^2 y^3 / z^4]
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