5r=75
r=75/5=15
3f=75
f=75/3
f=25
4d=75
d=75/4
d=18.9
5r+3d+4f+75
By some properties of logarithms, rewrite the equation as
so that
(<em>a</em> - 2<em>b</em>)² = <em>ab</em>
Expand the left side:
<em>a</em> ² - 4<em>ab</em> + 4<em>b</em> ² = <em>ab</em>
Rearrange terms to get a quadratic equation in <em>a</em>/<em>b</em> :
<em>a</em> ² - 5<em>ab</em> + 4<em>b</em> ² = 0
<em>b</em> must be greater than 0, otherwise log(<em>b</em>) doesn't exist, and the same goes for <em>a</em>. So we can divide by <em>b</em> ² to get
<em>a</em> ²/<em>b</em> ² - 5<em>a</em>/<em>b</em> + 4 = 0
Factorize and solve for <em>a</em>/<em>b</em> :
(<em>a</em>/<em>b</em> - 4) (<em>a</em>/<em>b</em> - 1) = 0
==> <em>a</em>/<em>b</em> = 4 or <em>a</em>/<em>b</em> = 1
However, if <em>a</em>/<em>b</em> = 1, then <em>a</em> = <em>b</em> makes <em>a</em> - 2<em>b</em> = -<em>b</em>. But we must have <em>b</em> > 0, so we omit the second solution and end up with
<em>a</em>/<em>b</em> = 4
Answer:
Step-by-step explanation:
I don not understand what is for 4 here. So there are 2 cases:
Case 1: If you mean: log[4(x+20)]= 3
We know 3 = log(10^3)= log(1000)
So we have log[4(x+20)]= log(1000)
so 4(x+20)= 1000
and x+20 = 1000/4
x+20 = 250 and finally x= 250-20, x=230
The solution is 230.
Case 2; If you mean that 4 is the base of logarithm.
and we know that
So we have
and x+20 = 81
or x= 81-20
x=61
The answer is 61.
Hope that useful for you, both cases.
(3.5,-8) I used the midpoint formula to find my answer
Answer: -4
Step-by-step explanation:
Combine r and −5r to get −4r.
dr/d (−4r)
The derivative of nax
is nax n−1 .
−4r 1−1
Subtract 1 from 1.
−4r0
For any term t except 0, t0
=1.
−4