MATHEMATICS HIGH SCHOOL

Solve 2 log2 2 + 2 log2 6 − log2 3x = 3.

Answers

Answer 1

Answer:

Answer:

x = 6

Step-by-step explanation:

Given : $2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3$

We have to solve the given expression $2\:log_2\:2\:+\:2\:log_26−\:log_2\:3x\:=\:3$

Subtract $2\log _2\left(2\right)+2\log _2\left(6\right)$ both sides , we have,

$2\:log_2\:2\:+\:2\:log_26-\:log_2\:3x-(2\log _2\left(2\right)+2\log _2\left(6\right)):=\:3-(2\log _2\left(2\right)+2\log _2\left(6\right))$

Simplify, we have,

$\log _2\left(3x\right)=3-2\log _2\left(2\right)-2\log _2\left(6\right)$

Divide both side by -1, we have,

$(-\log _2\left(3x\right))/(-1)=(3)/(-1)-(2\log _2\left(2\right))/(-1)-(2\log _2\left(6\right))/(-1)$

Simplify, we have,

$\log _2\left(3x\right)=-3+2\log _2\left(2\right)+2\log _2\left(6\right)$

Apply log rule, $a=\log _b\left(b^a\right)$

$2\log _2\left(6\right)-1=\log _2\left(2^(2\log _2\left(6\right)-1)\right)=\log _2\left(18\right)$

When log have same base,

$\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)$

$\mathrm{For\:}\log _2\left(3x\right)=\log _2\left(18\right)\mathrm{,\:\quad solve\:}3x=18$

3x = 18

x = 6

Answer 2

Answer: log(base2)[2² * 6² / 3x] = 3
144 / 3x = 2^3 = 8
144/8 = 3x
18 = 3x
x = 6

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Which choice is the explicit formula for the following geometric sequence

Answers

Answer:

B: $a_n= 0.2(-0.3)^(n-1)$

Step-by-step explanation:

Geometric sequence

0.2, -0.06, 0.018,-0.0054,0.00162....

General explicit formula is $a_n= a_1(r)^(n-1)$

Where r is the common ratio and a1 is the first term

a1 is 0.2 (first term)

we need to find out common ratio 'r'

To find 'r' divide second term by first term

$(-0.06)/(0.2) =-0.3$

Plug in the values in the general formula

$a_n= a_1(r)^(n-1)$

$a_n= 0.2(-0.3)^(n-1)$

Hello,

2/10,-6/100,18/1000,-54/10000,162/100000;...

a(n+1)/a(n)=-3/10
a(0)=2/10*1

a(n)=2/10* (-3/10)^(n-1)

Answer B

Using the graph
Order the lines from the steepest slope to the least steel slope

Answers

Answer:

B, A, C, D

Step-by-step explanation:

rise over run

slope: the ratio of the change in the dependent values (outputs) to the change in the independent values (inputs) between two points on a line

Answer:

The steepest slope is that of the line that is closest to being vertical.

Step-by-step explanation:

Hope this helps!!!!

Evaluate 3(a + b + c)2 for a = 2, b = 3, and c = 4.
54
243
729

Answers

6(9) is equal to 54
Answer: 54

First, do a+b+c.
a+b+c=2+3+4
=9

Then, multiply that answer by 3:
3x9=27

Evaluate b2c-1 for b = 8 and c = -4. -16 1/16 16 256

Answers

Answer: The correct option is (B) -16.

Step-by-step explanation: We are given to evaluate the value of the following expression for b = 8 and c = -4 :

$E=b^2c^(-1).$

To find the value of expression (i), we need to substitute the values of b and c in equation (i).

We will be using the following property of exponents :

$x^(-a)=(1)/(x^a).$

Therefore, from equation (i), we get

$E\n\n=b^2c^(-1)\n\n=8^2* (-4)^(-1)\n\n\n=(64)/(-4)\n\n=-16.$

Thus, option (B) is correct.

b²c-¹ = (8)²(–4)-¹ = 64(–¼) = –16

Help please!!!!!! it’s due soon

Answers

Because for perimeter you add all the sides up

What times what equals 8,000

Answers

4,000 × 2 = 8,000 hope thats what you meant!

4,000 • 2 = 8,000
Hope this helps!

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