Please help! ive been stuck on this for three weeks Use your calculator to find the smallest solution ot -5e^(-4x+2)+3=1/2log(x^(2)+1) and describe the steps you used. Round your answer to three decimals.

Step-by-step explanation:

Solution to Question 1

y = Log(x) if and only if

x = 10y

Interchange x and y

y = 10x

Hence

f -1(x) = 10x

Solution to Question 2

Use the change of base formula to write

Log4 65 = ln(65) / ln(4)

Then use a calculator

= 3.01 (rounded to 2 decimal places)

Solution to Question 3

Rewrite equation using 16 = 24

2 3x - 1 = 24

The two bases of the exponential expressions in the above equation are equal to 2. Hence their exponents has also to be equal

3x - 1 = 4

Solve for x

x = 5/3

Solution to Question 4

Logx 9 = 2 if and only if

x 2 = 9

x 2 = 32

For the above exponential expressions to be equal, their bases must be equal. Hence

x = 3

Solution to Question 5

Expand the polynomials on the right side

x 2 + kx - 6 = x 2 + x - 6

For two polynomials to be equal, all their corresponding coefficients must be equal. Hence

k = 1

Solution to Question 6

Write y in vertex form by completing the square

y = 2x 2 + 8x - 3 = 2(x 2 + 4x + 4 - 4) - 3

= 2(x 2 + 4x + 4) - 8 - 3

= 2(x + 2)2 - 11 which is of the form a(x - h)2 + k

vertex at (-2 , -11)

Solution to Question 7

Checking the given roots by substituting in equations A., B., C. and D. shows that D. is the equation with roots 3 and 5.

Solution to Question 8

We first note that

(x + 2)(x - 4) = x 2 - 2x - 8

We now multiply all terms of the given equation by (x + 2)(x - 4) and simplify to get

x (x - 4) + 3 (x + 2)= (4x + 2)

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation:

its a trick question

step-by-step explanation:

dogs love water, just turn on the hose and it will run in circles chasing the water all day : )