Question

Evaluate using logarithm table 0.925^3÷√0.673

Answer 1

Deduce the root of 3x(4-x)=5(x-2)

Answer 2

Find the roots of the equation 3x(4-x)=0

Answer 3

To evaluate the expression using a logarithm table, we need to first rewrite it as a logarithmic expression.

0.925^3 ÷ √0.673

We have an exponent and a square root, so let's break it down step by step:

Step 1: Convert the exponent into a logarithm.

0.925^3 becomes log_0.925(0.925^3)

Step 2: Simplify the square root.

√0.673 becomes 0.673^(1/2)

Step 3: Combine the logarithm and simplified square root.

Our expression becomes:

log_0.925(0.925^3) ÷ 0.673^(1/2)

Now, we can use a logarithm table to evaluate this expression. However, without the specific logarithm table, it is not possible to proceed further.

Answer 4

To deduce the root(s) of the equation 3x(4-x) = 5(x-2), we need to simplify and solve for x.

Expanding the equation, we get:

12x - 3x^2 = 5x - 10

Next, let's bring all the terms to one side of the equation:

3x^2 + (5x - 12x) - 5x + 10 = 0

Simplifying further, we obtain:

3x^2 - 12x + 10 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 3, b = -12, and c = 10.

We can now solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values of a, b, and c, we get:

x = (-(-12) ± √((-12)^2 - 4(3)(10))) / (2(3))

Simplifying:

x = (12 ± √(144 - 120)) / 6

x = (12 ± √24) / 6

x = (12 ± 2√6) / 6

Simplifying further:

x = 2 ± √6 / 3

Hence, the root(s) of the equation 3x(4-x) = 5(x-2) is/are x = (2 ± √6) / 3.

Answer 5

To find the roots of the equation 3x(4-x) = 0, we need to set the equation equal to zero and solve for x.

3x(4-x) = 0

We have two factors, 3x and (4-x), and to satisfy the equation, either one or both of these factors must equal zero.

Setting 3x = 0:

x = 0

Setting (4-x) = 0:

4 - x = 0
x = 4

So the roots of the equation are x = 0 and x = 4.