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V125BC [204]
3 years ago
6

Ln a+3 + ln a-3 = ln 16

Mathematics
1 answer:
Lilit [14]3 years ago
7 0
\bf log_{{  a}}(xy)\implies log_{{  a}}(x)+log_{{  a}}(y)\\\\
and\qquad \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
ln(a+3)+ln(a-3)=ln(16)\implies ln[(a+3)(a-3)]=ln(16)
\\\\\\
ln[a^2-3^2]=ln(16)\impliedby \textit{removing ln() from both sides}
\\\\\\
a^2-9=16\implies a^2=16+9\implies a^2=25
\\\\\\
a=\pm\sqrt{25}\implies a=\pm 5
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is the equation a true statement when x equals -3 in other words is -3 a solution to the equation 6 x + 5 = 5x +8 + 2x explained
serg [7]

Answer: Yes

Step-by-step explanation: bc 6(-3)+5=5(-3)+8+2(-3)

Becomes -18+5=-15+8+-6 which equals -13 on both sides meaning -3 is a solution

5 0
3 years ago
Read 2 more answers
​
DedPeter [7]

Answer:

The solution is (3/8, -7/8).

Step-by-step explanation:

y = −5x + 1

y = 3x − 2

Since  the 2 expressions in x are both equal to y :

−5x + 1  = 3x - 2

-5x - 3x = -2 - 1

-8x = -3

x = 3/8.

So y = 3x - 2

= 3(3/8) - 2

= 9/8 - 2 = -7/8.

6 0
3 years ago
Dexter has worked out 3/5 x 8 here is his working. explain the mistake he has made.
Tcecarenko [31]

Answer:

He multiplyed 3x8 and 5x8 when it should be 3x8 and 5x1 because you but 1 under the 8 to make it into a  fraction.

Step-by-step explanation:

8 0
2 years ago
Find the area of a circle whose area equals the half of the sum of the areas of two circles with radil 2 and 3.
OlgaM077 [116]

Step-by-step explanation:

step 1. a circle with r = 2 has area of (pi)r^2 = (pi)(4) = 4pi

step 2. a circle with r = 3 has area of (pi)r^2 = (pi)(9) = 9pi

step 3. the area, A, of a circle is half the sum of the area of the circles with r = 2 and r = 3

step 4. A = (4pi + 9pi)/2 = 13pi/2 = 6.5(pi).

step 5. the answer is not 6.5 but is 6.5(pi) or 6.5 times pi.

8 0
3 years ago
Tell weather the two rates form a proportion. help
Sindrei [870]
7/9 = 42/54...when 42/54 reduces, it becomes 7/9...so this is proportional because proportions are nothing but equivalent fractions.

u could also check it this way...
12/21 = 15/24
cross multiply
(21)(15) = (12)(24)
315 = 288.....these do not equal and are therefore, not proportionate

440/4 = 300/3
110 = 100....not equal, so not proportionate

120/5 = 88/4
24 = 22.....not proportionate

66/82 = 99/123
0.804 = 0.804.......these are proportional

68/172 = 43/123
0.395 = 0.349......nope, not proportional




6 0
3 years ago
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