You can take the log of the left and right hand side, and then apply the <span>logarithm rules:
log(a</span>ˣ) = x·log(a)
log(ab) = log(a) + log(b)
log(9^(x-1) * 2^(2x+2)) = log(6^(3x))
log(9^(x-1)) + log(2^(2x+2)) = 3x log(6)
(x-1) log(9) + (2x+2) log(2) - 3x log(6) = 0
x(log9 + 2log2 - 3log6) = log9 - 2log2
x = (log9 - 2log2) / (log9 + 2log2 - 3log6)
simplifying by writing log9 = 2log3 and log6 = log2+log3
x= 2(log3 - log2) / (2log3 + 2log2 - 3log2 - 3log3) =
x= -2(log3 - log2) / (log3 + log2) = -2 log(3/2) / log(6)
So 6^x = 4/9
Answer:
x is all real numbers
Step-by-step explanation:
6 + 5|2x -3| ≥ 4
The first step is to subtract 6 from each side
6 -6+ 5|2x -3| ≥ 4-6
5|2x -3| ≥ -2
Now divide each side by 5
5/5|2x -3| ≥ -2/5
|2x -3| ≥ -2/5
Absolute values are always positive. Our absolute value is greater than a negative number. It is always true. X can be any number and our absolute value will still be greater than -2/5.
x is all real numbers
(0,-9) is the y intercept
Answer:
C
Step-by-step explanation:
