This is a problem you need to solve using logs. When you use logs you can "pull" the exponents down in front of the log to get a new equation that looks like this: 2x^3 + x^2 log 81 = 6x - 3 log 27. Now divide both sides by log 81 and 6x - 3 simultaneously to get (2x^3 + x^2)/(6x - 3) = (log 27)/(log 81). If you do the log math on the right side you get .75. Now multiply both sides by 6x-3 to get 2x^3+x^2 = .75(6x-3). If you distribute that out on the left side you'll get 2x^3+x^2=4.5x-2.25. Now move everything over to the left side and set the whole thing equal to 0: 2x^3+x^2-4.5x+2.25=0. When you solve for x, you are in essence factoring, so do this by grouping: x^2(2x+1)-2.25(2x+1). Now finally factor out the 2x+1 to get (2x+1)(x^2-2.25). You're not done yet though cuz you need to solve each of those for x: 2x+1=0, and x= -1/2; x^2=2.25, and x=+/- 1.5. So all the values for x here are -1/2, 1.5, and -1.5
Answer:
(0,9) (-1,0), (2,0), (3,0),
Step-by-step explanation:
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Answer:
Exponential Function; base = 7; initial value = - 9.3
Step-by-step explanation:
Base is a number/value which has a variable exponent;
Initial value is the value of a function (i.e. y) when the independent variable, i.e. x, is equal to 0.
1 1/4
Pretty easy. For me at least.
Answer:
Step-by-step explanation:
The given expression is,
We apply the laws of indices to rewrite as a positive index to get,
We substitute
to obtain,
This simplifies to,
