Answer:
![x=-0.75](https://tex.z-dn.net/?f=x%3D-0.75)
Step-by-step explanation:
The given equation is
![4^{-5x-7}=6^{2x-1}](https://tex.z-dn.net/?f=4%5E%7B-5x-7%7D%3D6%5E%7B2x-1%7D)
We take logarithm of both sides to base 10.
![\log(4^{-5x-7})=\log(6^{2x-1})](https://tex.z-dn.net/?f=%5Clog%284%5E%7B-5x-7%7D%29%3D%5Clog%286%5E%7B2x-1%7D%29)
![(-5x-7)\log(4)=(2x-1)\log(6)](https://tex.z-dn.net/?f=%28-5x-7%29%5Clog%284%29%3D%282x-1%29%5Clog%286%29)
We expand the brackets to get;
![-5x\log(4)-7\log(4)=2x\log(6)-\log(6)](https://tex.z-dn.net/?f=-5x%5Clog%284%29-7%5Clog%284%29%3D2x%5Clog%286%29-%5Clog%286%29)
Group similar terms;
![-7\log(4)+\log(6)=2x\log(6)+5x\log(4)](https://tex.z-dn.net/?f=-7%5Clog%284%29%2B%5Clog%286%29%3D2x%5Clog%286%29%2B5x%5Clog%284%29)
![-7\log(4)+\log(6)=(2\log(6)+5\log(4))x](https://tex.z-dn.net/?f=-7%5Clog%284%29%2B%5Clog%286%29%3D%282%5Clog%286%29%2B5%5Clog%284%29%29x)
![\frac{-7\log(4)+\log(6)}{(2\log(6)+5\log(4))}=x](https://tex.z-dn.net/?f=%5Cfrac%7B-7%5Clog%284%29%2B%5Clog%286%29%7D%7B%282%5Clog%286%29%2B5%5Clog%284%29%29%7D%3Dx)
![x=-0.752478](https://tex.z-dn.net/?f=x%3D-0.752478)
To the nearest hundredth.
![x=-0.75](https://tex.z-dn.net/?f=x%3D-0.75)
When we say cubic root, it means that the exponent of your divisor is three. You can solve this by counting how many three's are there in a ten. So there are three three's. the other x has an exponent one and therefore is denoted by ∛x. The answer would be x³∛x.
Answer:
Jamie account will be 25042.5 in 14 years.
Step-by-step explanation:
K:P=2:5
P+75 it is 4:15
at first, P=5 units
so we have
2:5 and 4:15
since the K units didn't change we conver them to the same
2:5 times 2:2=4:10
so from 4:10 to 4:15 is a change of 75 in the right side
therefor 75=5 units so 75/5=15/1= 1 unit
so at first K=4 units=4 times 1 unit=4 times 15=60
P=10 units so 10 times 15=150
at first
Karen=60
Patricia=150