we can want some logarithm regulations: product rule, means rule, quotient rule. means rule: log(a^b) = b log(a) Product rule: log(a*b) = log(a) + log(b) Quotient rule: log(a/b) = log(a) - log(b) f(x) = 3[lnx - 2ln(x+a million) - ln(x-a million)] word the means rule in opposite on the 2d term. f(x) = 3[lnx - ln([x+a million)^2] - ln(x-a million)] f(x) = 3[ln(x / [(x+a million)^2 (x-a million)])] f(x) = ln[(x / [(x+a million)^2 (x-a million)])^3] increasing and simplifying the stuff interior the middle does not look like it could help any.
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Verified answer
ln(x^2 - 9) - ln(x + 3)
use natural log property: ln x - ln y = ln x/y
= ln[(x^2 - 9) / (x + 3)]
factor x^2 - 9 (difference of two squares)
= ln[(x + 3)(x - 3) / (x + 3)]
simplify
= ln(x - 3)
Going back to basic log rules:
log(m/n) = log(m) - log(n)
so, in your case:
ln(x^2 - 9) - ln (x + 3) becomes:
ln((x^2 - 9) / (x + 3))
Simplify that by expanding (x^2 - 9), and then cancelling out the (x+3)s, you get
ln(x - 3)
Btw - I assumed you mean ln(x^2 - 9) as opposed to ln(2x - 9)
ln(x^2 -9) - ln(x+3)
law of ln a-b =ln a/b
ln(x^2 -9 / x+3)
x^2 - 9 = (x+3) (x-3) simplify
(x+3)(x-3) / (x+3)
= ln(x-3)
I believe it would be y=ln(x2-9/x+3)
we can want some logarithm regulations: product rule, means rule, quotient rule. means rule: log(a^b) = b log(a) Product rule: log(a*b) = log(a) + log(b) Quotient rule: log(a/b) = log(a) - log(b) f(x) = 3[lnx - 2ln(x+a million) - ln(x-a million)] word the means rule in opposite on the 2d term. f(x) = 3[lnx - ln([x+a million)^2] - ln(x-a million)] f(x) = 3[ln(x / [(x+a million)^2 (x-a million)])] f(x) = ln[(x / [(x+a million)^2 (x-a million)])^3] increasing and simplifying the stuff interior the middle does not look like it could help any.
ln(x^2 - 9) - ln(x + 3)
.......x^2 - 9
=ln[--------------]
........x + 3
.......(x + 3)(x - 3)
=ln[---------------------] cancel x + 3
............x + 3
=ln(x - 3) answer//