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Solve the equation 3x^2 – 14x = 5

Write as the logarithm of a single number: 3 log 2 – log 4

Thankyou.

1) Solve the equation 3x^2 – 14x = 5

3x^2 - 14x - 5 = 0

Factorise:

(3x+1)(x-5) = 0

x = -1/3 or x = 5

2) Write as the logarithm of a single number: 3 log 2 – log 4

3 log 2 = log 2^3 = log 8

log 8 - log 4 = log (8/4) = log 2

3x^2 -14x = 5
rewrite as:
3x^2 - 14x - 5 = 0
to find the roots of the equation ax^2 + bx + c = 0 use the formulas r1 =( -b + sqrt(b^2 - 4ac) )/2a and r2 = ( -b - sqrt(b^2 - 4ac) )/2a
applied to the above equation this yields the two roots r1 = 5 and r2 = -2/6 = -1/3

3log2 - log4

First some identities:

alogb = log(b^a)
log(ab) = loga + logb
log(a/b) = loga - log b

Thus 3log2 = log(2^3) = log8
So 3log2 -log4 = log8-log4 = log(8/4) = log2

3x^2-14x=5
3x^2-14x-5=0
(3x+1)(x-5)

x=-1/3 and 5