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:
b: 261,763
Step-by-step explanation:
do the parenthesis then mutiply the 2 #s
You deposit some money into a bank account paying 8% simple interest per year. You received $500 in interest after 2 years. How much the deposit (principal) was?
Result
The principal was $3125.
Explanation
Find principal by using the formula I=P⋅i⋅t, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.
In this example I = $500, i = 8% and t = 2 years, so
IPPP=P⋅i⋅t=Ii⋅t=5000.08⋅2=3125
Answer:
The number being multiplied by
x
is the slope of the line. So, the slope of the line is calculated by rise/run. The rise is how up or down it goes from a certain point to another, and the run is how right or left it goes from a certain point to the other.
Answer:
If Andrea plays eight games at the arcade and wins 20 tickets per game then 8 x 20= 160.
If Andrea plays nine games at the arcade and wins 20 tickets per game then 9×20 = 180.
A= 9 games
Step-by-step explanation:
