QUESTION 11
Given : ![\ln(3x-8)=\ln(x+6)](https://tex.z-dn.net/?f=%5Cln%283x-8%29%3D%5Cln%28x%2B6%29)
We take antilogarithm of both sides to get:
![3x-8=x+6](https://tex.z-dn.net/?f=3x-8%3Dx%2B6)
Group similar terms to get:
![3x-x=6+8](https://tex.z-dn.net/?f=3x-x%3D6%2B8)
Simplify both sides to get:
![2x=14](https://tex.z-dn.net/?f=2x%3D14)
Divide both sides by 2 to obtain:
![x=7](https://tex.z-dn.net/?f=x%3D7)
12. Given; ![\log_3(9x-2)=\log_3(4x+3)](https://tex.z-dn.net/?f=%5Clog_3%289x-2%29%3D%5Clog_3%284x%2B3%29)
We take antilogarithm to obtain:
![(9x-2)=(4x+3)](https://tex.z-dn.net/?f=%289x-2%29%3D%284x%2B3%29)
Group similar terms to get:
![9x-4x=3+2](https://tex.z-dn.net/?f=9x-4x%3D3%2B2)
![5x=5](https://tex.z-dn.net/?f=5x%3D5)
We divide both sides by 5 to get:
![x=1](https://tex.z-dn.net/?f=x%3D1)
13. ![\log(4x+1)=\log25](https://tex.z-dn.net/?f=%5Clog%284x%2B1%29%3D%5Clog25)
We take antilogarithm to get:
![(4x+1)=25](https://tex.z-dn.net/?f=%284x%2B1%29%3D25)
Group similar terms
![4x=25-1](https://tex.z-dn.net/?f=4x%3D25-1)
![4x=24](https://tex.z-dn.net/?f=4x%3D24)
Divide both sides by 4
![x=6](https://tex.z-dn.net/?f=x%3D6)
14. Given ; ![\log_6(5x+4)=2](https://tex.z-dn.net/?f=%5Clog_6%285x%2B4%29%3D2)
We take antilogarithm to get:
![(5x+4)=6^2](https://tex.z-dn.net/?f=%285x%2B4%29%3D6%5E2)
Simplify:
![(5x+4)=36](https://tex.z-dn.net/?f=%285x%2B4%29%3D36)
![5x=36-4](https://tex.z-dn.net/?f=5x%3D36-4)
![5x=32](https://tex.z-dn.net/?f=5x%3D32)
Divide both sides by 5
![x=\frac{32}{5}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B32%7D%7B5%7D)
Or
![x=6\frac{2}{5}](https://tex.z-dn.net/?f=x%3D6%5Cfrac%7B2%7D%7B5%7D)
15. Given: ![\log(10x-7)=3](https://tex.z-dn.net/?f=%5Clog%2810x-7%29%3D3)
We rewrite in the exponential form to get:
![(10x-7)=10^3](https://tex.z-dn.net/?f=%2810x-7%29%3D10%5E3)
![(10x-7)=1000](https://tex.z-dn.net/?f=%2810x-7%29%3D1000)
![10x=1000+7](https://tex.z-dn.net/?f=10x%3D1000%2B7)
![10x=1007](https://tex.z-dn.net/?f=10x%3D1007)
Divide both sides by 10
![x=\frac{1007}{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1007%7D%7B10%7D)
16. Given: ![\log_3(4x+2)=\log_3(6x)](https://tex.z-dn.net/?f=%5Clog_3%284x%2B2%29%3D%5Clog_3%286x%29)
We take antilogarithm to obtain:
![(4x+2)=(6x)](https://tex.z-dn.net/?f=%284x%2B2%29%3D%286x%29)
![2=6x-4x](https://tex.z-dn.net/?f=2%3D6x-4x)
Simplify
![2=2x](https://tex.z-dn.net/?f=2%3D2x)
Divide both sides by 2
![1=x](https://tex.z-dn.net/?f=1%3Dx)
17. Given
.
We rewrite in exponential form:
![(3x+12)=2^4](https://tex.z-dn.net/?f=%283x%2B12%29%3D2%5E4)
![(3x+12)=16](https://tex.z-dn.net/?f=%283x%2B12%29%3D16)
![3x=16-12](https://tex.z-dn.net/?f=3x%3D16-12)
![3x=4](https://tex.z-dn.net/?f=3x%3D4)
Divide both sides by 3
![x=\frac{4}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%7D%7B3%7D)
18. Given ![\log_3(3x+7)=\log_3(10x)](https://tex.z-dn.net/?f=%5Clog_3%283x%2B7%29%3D%5Clog_3%2810x%29)
We take antilogarithm to get:
![(3x+7)=(10x)](https://tex.z-dn.net/?f=%283x%2B7%29%3D%2810x%29)
Group similar terms:
![7=10x-3x](https://tex.z-dn.net/?f=7%3D10x-3x)
![7=7x](https://tex.z-dn.net/?f=7%3D7x)
We divide both sides by 7
![x=1](https://tex.z-dn.net/?f=x%3D1)
19. Given: ![\log_2x+\log_2(x-3)=2](https://tex.z-dn.net/?f=%5Clog_2x%2B%5Clog_2%28x-3%29%3D2)
Apply the product rule to simplify the left hand side
![\log_2x(x-3)=2](https://tex.z-dn.net/?f=%5Clog_2x%28x-3%29%3D2)
We take antilogarithm to obtain:
![x(x-3)=2^2](https://tex.z-dn.net/?f=x%28x-3%29%3D2%5E2)
![x^2-3x=4](https://tex.z-dn.net/?f=x%5E2-3x%3D4)
![x^2-3x-4=0](https://tex.z-dn.net/?f=x%5E2-3x-4%3D0)
![(x-4)(x+1)=0](https://tex.z-dn.net/?f=%28x-4%29%28x%2B1%29%3D0)
x=-1 or x=4
But x>0, therefore x=4
20. Given
Apply product rule to the LHS
Rewrite in the exponential form to get:
This implies that:
or ![x=2.91](https://tex.z-dn.net/?f=x%3D2.91)
Answer:
B i think
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Answer:
ha fae 43-10kape kaoe lap qe us HSdif
Step-by-step explanation:
Answer:
y intercept = 0
equation: y=26x
Step-by-step explanation:
just look at the graph lol
Yw! :D