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4 years ago

What is the sum of 5 and a number x

Mathematics

1 answer:

11Alexandr11 [23.1K]4 years ago

4 0

5+x
Don't you have any other information?

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Log(x-2)+log2=2logy<br>log(x-3y+3)=0

In-s [12.5K]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right$

$===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}$

$\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac$

$y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D$

$\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D$

4 0

3 years ago

Given the fu8nction f(x) = 2(x + 10), find x if f(x) = 24.<br><br> A) 68<br> B) 7<br> C) 17<br> D) 2

lyudmila [28]

F(x)=2(x+10)=24
2(x+10)=24
divide 2
x+10=12
minus 10
x=2
D

6 0

3 years ago

What is the following product? (2 square root 7+3 square root 6)(5 square root 2+4 square root 3)

Xelga [282]

$(2\sqrt7+3\sqrt6)(5\sqrt2+4\sqrt3)\qquad\text{use distributive property}\\\\=(2\sqrt7)(5\sqrt2)+(2\sqrt7)(4\sqrt3)+(3\sqrt6)(5\sqrt2)+(3\sqrt6)(4\sqrt3)\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt{12}+12\sqrt{18}\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt{4\cdot3}+12\sqrt{9\cdot2}\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt4\cdot\sqrt3+12\sqrt9\cdot\sqrt2\\\\=10\sqrt{14}+8\sqrt{21}+(15)(2)\sqrt3+(12)(3)\sqrt2\\\\=\boxed{10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2}$

5 0

3 years ago

Read 2 more answers

I will mark BRAINLIEST if your answer is accurate!

Mila [183]

Answer:

i would say A. or B. most likely B

Step-by-step explanation:

7 0

4 years ago

Given the problem below what mistake did Bob make in solving the equation? Bob and his friends paid $30 for 3 sandwiches and and

storchak [24]

Answer:

Bob forgot to distribute 3 to 1.50 in the parentheses

Step-by-step explanation:

Bob made the mistake in his first step.

In the equation 3(x + 1.50) = 30, the 3 has to be distributed to both x and 1.50.

But, Bob only distributed it to x, which led him to get the wrong answer.

So, Bob's mistake when solving was that he forgot to distribute the 3 to 1.50

7 0

3 years ago