An important rule of logs is a*log b = log b^a.
Thus, 2 (log to the base 5 of )(5x^3) = (log to the base 5 of ) (5x^3)^2, or
(log to the base 5 of ) (25x^6).
Next, (1/3) (log to the base 5 of ) (x^2+6) = (log to the base 5 of ) (x^2+6)^(1/3).
Here, the addition in the middle of the given expression indicates multiplication:
2Log5(5x^3)+1/3log5(x^2+6) = (log to the base 5 of ) { (5x^3)^2 * (x^2+6)^(1/3) }.
Here we've expressed the given log quantity as a single log.
Answer:
-3
Step-by-step explanation:
-3/8÷3/4
=-3/8×4/3
=-6/2
=-3
At firt we should solve what is h(0)
h(0)=0^2+2
h(0)=2
So then you should take the h(0) answer to g(x) and the result is g(2)= -2-5=-7
Answer:
<u>f(x) = = (x + √2 i) (x - √2 i) (x - 2 ) (x + 1)</u>
Step-by-step explanation:
The given function is f(x) = x⁴ - x³ -2x -4
factor the polynomial function
f(x) = x⁴ - x³ -2x -4 = (x⁴ - 4) - (x³ + 2x ) ⇒ take (-) as a common from (- x³ -2x)
= (x² + 2 ) (x² - 2) - x (x² + 2) ⇒ take (x² + 2) as a common
= (x² + 2 ) ( x² - x - 2)
= (x + √2 i) (x - √2 i) (x -2 ) ( x+1)
Notes: (x⁴ - 4) = (x² + 2 ) (x² - 2)
(x² + 2)= (x + √2 i) (x - √2 i)
( x² - x - 2) = (x -2 ) ( x+1)
Answer:
First one: C. Second One:C.
Step-by-step explanation:
Kate purchased a car for $23,000. It will depreciate by a rate of 12% a year. What is the value of the car in 4 years?
a) $13,935.76
b) $12,874.57
c) $13,792.99
To solve this this is an exponential function. The price started at $23,000 and depreciates at 12% so the equation is f(x) = (23,0000)(1-0.12)^4. When calculated results with 13792.99328 which is C.
A rare coin is currently worth $450. The value of the coin increases 4% each year. Determine the value of the coin after 7 years.
a) $613.98
b) $546.78
c) $592.17
To solve this this is also an exponential function. The price started at $450 and the coin increases 4% each year so the equation is f(x) = (450)(1+0.04)^7. When calculated results with 592.169300656 which is c.
