1/3 ln(<em>x</em>) + ln(2) - ln(3) = 3
Recall that 
, so
ln(<em>x</em> ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
Then
ln(2/3 <em>x</em> ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant <em>e</em>. (I'm using exp(<em>x</em>) = <em>e</em> ˣ so I can write it all in one line.)
exp(ln(2/3 <em>x</em> ¹ʹ³)) = exp(3)
Now exp(ln(<em>x</em>)) = <em>x </em>for all <em>x</em>, so this simplifies to
2/3 <em>x</em> ¹ʹ³ = exp(3)
Now solve for <em>x</em>. Multiply both sides by 3/2 :
3/2 × 2/3 <em>x</em> ¹ʹ³ = 3/2 exp(3)
<em>x</em> ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(<em>x</em> ¹ʹ³)³ = (3/2 exp(3))³
<em>x</em> = 3³/2³ exp(3×3)
<em>x</em> = 27/8 exp(9)
which is the same as
<em>x</em> = 27/8 <em>e</em> ⁹
Answer:
54
Step-by-step explanation:
Answer:
Step-by-step explanation:
1) Write 8x+14 as 2(4x+7) and now multiply by 1/2 so that we get 4x+7
2)Subtract 7 from both sides
4x+7=39
-7 -7
4x=32
3) Divide by 8
x=8
Thus we get x=8 as answer
So reasons are
i) Distributive property
ii) Subtraction property of equality
iii) Division property of equality
Answer:
Raoul estimated the difference to be: 89
97.23 --> 97
8.3 --> 8
97-8= 89
The actual difference is: 88.93
97.23-8.3 = 88.93
Answer:
Choice A
Step-by-step explanation:
In each case, each equation has an equation of a line in y = mx + b form equaling another equation of a line in y = mx + b form. If the two sides are equal, it is the same equation, there are infinitely many solutions. If the sides are different, then if the slopes are different, the lines intersect at one point, and there is exactly 1 solution. If the slopes are equal, the lines are parallel, and there is no solution.
(Choice A) -10x-10=-10x-10
In Choice A, both sides of the equation are equal, so there are infinitely many solutions.
(Choice B) 10x-10=-10x+10
(Choice C) 10x-10=-10x-10
(Choice D) -10x-10=-10x+10
In choices B through D, the two sides are not equal, so there is either 1 solution (B and C since they have different slopes) or no solution (D since the slopes are equal).
