Answer:help with what???
Step-by-step explanation:
Answer:
x=2ln(2)/(2ln(2)-ln(3))
Step-by-step explanation:
ln(4^x-1)=ln(3^x)
(x-1)ln(4)=ln(3^x)
(x-1)ln(4)=xln(3)
ln(4)x-ln(4)=xln(3)
ln(4)x=ln(3)x+2ln(2)
2ln(2)x-ln(3)x=2ln(2)
(2ln(2)-ln(3))x=2ln(2)
Therefore, x=2ln(2)/(2ln(2)-ln(3))
Answer:
Nice to hear that, congrats with practice 7.3
Answer:
the length of the rectangle is, 21 in.
Step-by-step explanation:
Area of the rectangle(A) is given by:
.....[1]
where,
l is the length of the rectangle
w is the width of the rectangle.
As per the statement:
The width of a rectangle is 9 in. shorter than its length.
⇒
It is also given that:
The area of the rectangle is 252 in².
⇒A = 252 in².
Substitute in [1] we have;

⇒
⇒
Factorize this equation:
Split the middle term;
⇒
⇒
⇒
By zero product property we have;
and 
⇒
and 
Since, length cannot be in negative
⇒
Therefore, the length of the rectangle is, 21 inches.
Answer:
51°
Step-by-step explanation:
Reference angle (θ) = ?
Opposite side length = 31
Hypotenuse length = 40
Apply SOH, which is;
Sin θ = Opp/Hyp
Plug in the values
Sin θ = 31/40
θ = sin^{-1}(31/40)
θ = 51° (neatest whole degree)