Question

I need help with this question... please look at the question on what is asking for you to do and can you put the answer choices in orderI just need 3,8,9,11,12,13,14

Answer 1

NO 3

`\begin{gathered} 2\log (y+5)=\log 20\text{ -log5} \\ \log (y+5)^2=\log ((20)/(5)) \\ (y+5)^2=4 \\ \text{square root both sides} \\ y+5\text{ =2} \\ y=2-5 \\ y=-3 \\ The\text{ right option is b} \end{gathered}`

N0 8

`\begin{gathered} \ln \text{ 8 +ln(n-9)=5ln2} \\ \ln ((n-9)*8)=\ln 2^5 \\ \ln (8n-72)=\ln 32 \\ 8n-72=32 \\ 8n\text{ = 32+72} \\ 8n=104 \\ n=(104)/(8) \\ n=13 \\ \text{Therefore the right answer is f} \end{gathered}`

No 9

`\begin{gathered} 5\ln (2a-1)\text{ =15} \\ \text{Divide both sides by 5} \\ \ln (2a-1)=3 \\ \text{Take the exponential value of both sides} \\ 2a-1=e^3 \\ 2a-1=20.0855 \\ 2a=1+20.0855 \\ 2a=21.0855 \\ \text{Divide both sides by 2} \\ a=(21.0855)/(2) \\ a=10.5428 \\ \text{The right option is }q \end{gathered}`

No 11

`\begin{gathered} ((1)/(8))^(2-2n)=16 \\ ((1)/(2^3))^(2-2n)=2^4 \\ 2^(-3(2-2n))=2^4 \\ 2^(-6+6n)=2^4 \\ -6+6n\text{ =4} \\ \text{collect like terms} \\ 6n=4+6 \\ 6n\text{ =10} \\ \text{Divide both sides by 6} \\ n=(10)/(6) \\ n=(5)/(3) \\ \text{Therefore the right answer is }j \end{gathered}`

No 12

`\begin{gathered} -3e^(2m-5)-7=-34 \\ \text{collect like terms} \\ -3e^(2m-5)=-34+7 \\ -3e^(2m-5)=-27 \\ \text{Divide both sides by -3} \\ e^(2m-5)=(-27)/(-3) \\ e^(2m-5)=9 \\ \text{Find the natural logarithm of both sides} \\ 2m-5\text{ =ln9} \\ 2m-5=2.1972 \\ 2m=5+2.1972 \\ 2m=7.1972 \\ \text{divide both sides by 2} \\ m=(7.1972)/(2) \\ m=\text{ 3.5986} \\ \text{Therefore, the right answer is, p} \end{gathered}`

N0 13

No 14

`\begin{gathered} \ln k-\ln 14=2 \\ \ln ((k)/(14))\text{ = 2} \\ Take\text{ the exponential of both sides} \\ (k)/(14)=e^2 \\ (k)/(14)=7.38906 \\ \text{crossmultiply} \\ k=14*7.38906 \\ k=103.4468 \\ \text{Therefore the right answer is, u} \end{gathered}`