9514 1404 393
Answer:
Explanation:
a) The equation written in standard form is ...
4y^2 -7y -15 = 0
We find the two factors of (4)(-15) that have a sum of -7 to be -12 and +5. Then the equation can be written and factored as ...
4y^2 -12y +5y -15 = 0
4y(y -3) +5(y -3) = 0
(4y +5)(y -3) = 0
The solutions to this equation are the values of y that make the factors zero:
4y +5 = 0 ⇒ y = -5/4
y -3 = 0 ⇒ y = 3
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b) Let y = 3^x. Then the equation transforms to ...
4((3^x)^2) = 15 +7(3^x)
4y^2 = 15 +7y . . . . . . . . . same equation as above, with the same solutions
Then the value of x is ...
log(y) = x·log(3)
x = log(y)/log(3) . . . . . . . . y > 0
The only useful solution of the ones found above is y = 3.
x = log(3)/log(3)
x = 1