Answer:
To solve an exponential equation, take the log of both sides, and solve for the variable.
Step-by-step explanation:
Example 1: Solve for x in the equation tex2html_wrap_inline119 .
Solution:
Step 1: Take the natural log of both sides:
displaymath121
Step 2: Simplify the left side of the above equation using Logarithmic Rule 3:
displaymath123
Step 3: Simplify the left side of the above equation: Since Ln(e)=1, the equation reads
displaymath127
Ln(80) is the exact answer and x=4.38202663467 is an approximate answer because we have rounded the value of Ln(80)..
Check: Check your answer in the original equation.
displaymath131
The answer is B because the x describes the domain and it can also be the input value
Answer:
D. 5/3
Step-by-step explanation:
![\frac{1/6+1/2+1/3+x}{4} =2/3](https://tex.z-dn.net/?f=%5Cfrac%7B1%2F6%2B1%2F2%2B1%2F3%2Bx%7D%7B4%7D%20%3D2%2F3)
![1/6+1/2+1/3+x=8/3](https://tex.z-dn.net/?f=1%2F6%2B1%2F2%2B1%2F3%2Bx%3D8%2F3)
![x=8/3-1/6-1/2-1/3](https://tex.z-dn.net/?f=x%3D8%2F3-1%2F6-1%2F2-1%2F3)
![x=8/3-1/6-3/6-2/6](https://tex.z-dn.net/?f=x%3D8%2F3-1%2F6-3%2F6-2%2F6)
![x=8/3-6/6](https://tex.z-dn.net/?f=x%3D8%2F3-6%2F6)
![x=16/6-6/6=10/6](https://tex.z-dn.net/?f=x%3D16%2F6-6%2F6%3D10%2F6)
simplified
![x=5/3](https://tex.z-dn.net/?f=x%3D5%2F3)
Hope this helps
![4x-8y=0 \\ \underline{-3x+8y=-7} \\ 4x-3x=0-7 \\ x=-7 \\ \\ 4x-8y=0 \\ 4 \times (-7)-8y=0 \\ -28-8y=0 \\ -8y=28 \\ y=\frac{28}{-8} \\ y=-\frac{7}{2} \\ \\ \left \{ {{x=-7} \atop {y=-\frac{7}{2}}} \right.](https://tex.z-dn.net/?f=4x-8y%3D0%20%5C%5C%0A%5Cunderline%7B-3x%2B8y%3D-7%7D%20%5C%5C%0A4x-3x%3D0-7%20%5C%5C%0Ax%3D-7%20%5C%5C%20%5C%5C%0A4x-8y%3D0%20%5C%5C%0A4%20%5Ctimes%20%28-7%29-8y%3D0%20%5C%5C%0A-28-8y%3D0%20%5C%5C%0A-8y%3D28%20%5C%5C%0Ay%3D%5Cfrac%7B28%7D%7B-8%7D%20%5C%5C%0Ay%3D-%5Cfrac%7B7%7D%7B2%7D%20%5C%5C%20%5C%5C%0A%20%5Cleft%20%5C%7B%20%7B%7Bx%3D-7%7D%20%5Catop%20%7By%3D-%5Cfrac%7B7%7D%7B2%7D%7D%7D%20%5Cright.%20)
There is one solution to this system of equations. The answer is B.