8. If 4x^+ 4x^ + 4x^ + 4x^ + 4 x^+ 4x^ + 4x^+ 4x^ =
1/512
then what is the value of-3/
х
Answers
Answer:
1/2
Step-by-step explanation:
Hello,
The problem that you wrote down can be simplified to look much cleaner, and thus, easier to understand. You have the addition of 4x eight times. This is the same as 8 (4x). We can set that equal to 1/512 and solve for x using logs.
8 (4x) = 1/512
Divde both sides by 8.
4x = 1/4096
Let's convert this into the form of log b y = x. 4 is your base, b. x is your x value. 1/4096 is y.
log 4 (1/4096) = x
You can look at this many ways, use your calculator, or use logic to solve for x. Remember that when you want to get a fraction like 1/4096, you need to raise a whole number to a negative value. How many times is 4 multiplied by itself to get 4096? 4 raised to the 6th power gives you 4096. To get 1.4096, we get x = -6.
x = -6.
Question: What is the value of -3/x ?
-3 / x = -3 / -6 = 1/2
Answer: 1/2