pH = f(x) = -log₁₀x
1. Graphs
I used Excel to calculate the pH values and draw the graphs (see the Figure).
f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.
The points at which pH = 0 and pH = 1 are indicated by the large red dots.
2. x = 0.5
When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.
3. Transformations
(a) ƒ(x) = -log(x) + 1
This function has no y-intercept, because log(0) is undefined.
(b) ƒ(x +1) = -log(x + 1)
f(0) = -log(0 + 1) = -log(1) = 0
This function has a y-intercept at (0,0).
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Answer:
1 cm = 20 km
so 3.5 cm would equal : 3.5 * 20 = 70 km
hope it helps ;)
Step-by-step explanation:
Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
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<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
25 people leaving $15 for the boat rental and that still leaves you a remainder of $10
Mercury the liquid metal? 674.1°F or 356.7°C
