Mathematics, 23.07.2019 20:00 lilloser

Solve the logarithmic equation. when necessary, round answer to the nearest hundredth. logx 36 = 2

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Answer from: gggggg47

x=6

Step-by-step explanation:

We have been given a logarithmic equation $\text{log}_x(36)=2$ . We are asked to solve our given equation.

Using log rule $\text{log}_a(b)=\frac{\text{ln}(b)}{\text{ln}(a)}$ , we will get:

$\text{log}_x(36)=\frac{\text{ln}(36)}{\text{ln}(x)}$

Substituting back this value, we will get:

$\frac{\text{ln}(36)}{\text{ln}(x)}=2$

Multiply both sides by $\text{ln}(x)$ :

$\frac{\text{ln}(36)}{\text{ln}(x)}\times\text{ln}(x)=2\times\text{ln}(x)$

$\text{ln}(36)=2\times\text{ln}(x)$

Switch sides:

$2\times\text{ln}(x)=\text{ln}(36)$

$2\times\text{ln}(x)=\text{ln}(6^2)$

Using property $\text{log}_a(x^b)=b\cdot \text{log}_a(x)$ , we will get:

$2\times\text{ln}(x)=2\cdot \text{ln}(6)$

$\frac{2\times\text{ln}(x)}{2}=\frac{2\cdot \text{ln}(6)}{2}$

$\text{ln}(x)=\text{ln}(6)$

Since base of both sides are equal, therefore, the value of x is 6.

Answer from: Quest

b: |12 – x| ≤ 0.25

step-by-step explanation:

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

Answer from: Quest

Answer: f(x) = -2x^3 +3x^2 +11x -6see attachedan infinite number. since the magnitude of the leading coefficient is not specified, it may be any negative number. (we have chosen the smallest magnitude integer that makes all coefficients be integers.)step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

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