What is the value of x?
1 answer:
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Answer:
a) 3
b) 9
c) 81
d) x
Step-by-step explanation:
We know the properties of log function as:
1) log(AB) = log(A) + log(B)
2)
3) log(aᵇ) = b × log(a)
also,
4)
Given:
a. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(3) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = 1 × log(3)
taking anti-log both sides
y = 3
b. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(9) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(9)
taking anti-log both sides
y = 9
c. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(81) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(81)
taking anti-log both sides
y = 81
d. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(x) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(x)
taking anti-log both sides
y = x
<h3>Answer:</h3>
- -100x +100; 3
- 5x +81; 162
The distributive property is your friend. It tells you ...
a(b + c) = ab + ac
It can also be used to simplify the product of binomials (or other polynomials).
(a +b)^2 = (a +b)(a +b) = a(a +b) + b(a +b) = a^2 +ab +ab +b^2
(a +b)^2 = a^2 +2ab + b^2 . . . . . . . worth remembering
1. (x -10)^2 -x(x +80) = (x^2 -20x +100) +(-x^2 -80x)
= -100x +100 . . . . . . simplified form
For the purposes of calculation, it can be easier to factor out 100:
= 100 (1 -x)
Then for x = 0.97
= 100(1 -0.97) = 100(0.03) = 3
___
2. (2x +9)^2 -x(4x +31) = (4x^2 +36x +81) -4x^2 -31x = 5x +81
For x = 16.2, this is ...
5(16.2) +81 = 81 +81 = 162
_____
The purpose of the attachment is to show the evaluation is correct.