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tigry1 [53]
2 years ago
5

Find the value of x which satisfies the following equation. log2(x−1)+log2(x+5)=4

Mathematics
1 answer:
weqwewe [10]2 years ago
4 0

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \: x = 3

____________________________________

\large \tt Solution  \: :

\qquad \tt \rightarrow \:  log_{2}(x - 1)  log_{2}(x + 5)  = 4

\qquad \tt \rightarrow \:  log_{2} \{(x - 1)(x + 5) \} = 4

[ log (x) + log (y) = log (xy) ]

\qquad \tt \rightarrow \: ( x - 1)(x + 5) =  {2}^{4}

\qquad \tt \rightarrow \:  {x}^{2}  + 5x - x - 5 =  16

\qquad \tt \rightarrow \:  {x}^{2}  + 4x - 5 - 16 = 0

\qquad \tt \rightarrow \:  {x}^{2}  + 4x -21 = 0

\qquad \tt \rightarrow \:  {x}^{2}  + 7x - 3x - 21 = 0

\qquad \tt \rightarrow \:  x(x + 7) - 3(x + 7) = 0

\qquad \tt \rightarrow \: (x + 7)(x - 3) = 0

\qquad \tt \rightarrow \: x =  - 7 \:  \: or \:  \: x = 3

The only possible value of x is 3, since we can't operate logarithm with a negative integer in it.

\qquad \tt \rightarrow \: x = 3

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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Step-by-step explanation:

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2 years ago
Y= x+8 <br> 2x+y=-10 <br><br> A. (2,6)<br> B. ( 2,-6)<br> C. ( -6,2)<br> D. (6,2)
alukav5142 [94]
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Find a formula for the function f(x) such that f′(x)=(ln(x))^2/x and f(2)=6
Rzqust [24]
F(x)= ∫ln²x/x dx= ∫ln²xd(lnx) cause d(lnx)= (lnx)'dx=1/x dx
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4 0
3 years ago
HELP ME HELP ME HELP ME!!! Given f(x) below, find f^-1(x).
elixir [45]

Answer:

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Step-by-step explanation:

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4y - 6 = - x ( multiply through by - 1 )

- 4y + 6 = x

Change y back into terms of x with x = f^{-1} (x) , then

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7 0
2 years ago
A diameter of a circle has endpoints P(-10,-2) and Q(4,6).
kompoz [17]

Answer:

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Step-by-step explanation:

a.  The center is the midpoint  of the diameter PQ.

= (-10+4)/2, (-2+6)/2

= (-3, 2).

b. The radius is the distance from the center to a point on the circle.

Take the point (4, 6):

The radius = √((-3-4)^2 + (2-6)^2)

= √65.

c.  The equation of the circle is:

Using the standard form

(x - h)^2 + (y - k)^2 = r^2  where  (h, k) is the center and r = the radius:

it is (x - (-3)^2 + (y - 2) = 65

= (x + 3)^2 + (y - 2)^2 = 65.

4 0
3 years ago
Read 2 more answers
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