Question

Help me solve this log54,log24,log0.8

Answer 1

Help me solve this:a composite solid consists of a cube of edge 28cm & square pyramid of height 16cm calculate the surface area of the solid

Answer 2

for the logs, all you have done is list three logs. So what is the question?

For the solid, the area of the cube is 5*28^2 (the top face is hidden)
the area of the pyramid is four triangle, each with base=28 and height=√60
I assume you can find the area of a triangle ...

Answer 3

[AI-generated answer — Explain Bot]

To solve the expressions log54, log24, and log0.8, we need to understand logarithms and how they work.

Logarithms are the inverse operation of exponentiation. In mathematics, a logarithm of a number x to a given base b is the exponent to which b must be raised to obtain x. This can be written as log_b(x) = y if b^y = x.

To evaluate logarithms, we usually use a base of 10, which is called the common logarithm and is denoted as log(x) or simply log10(x). However, it's important to note that logarithms can have any base.

Now let's solve the given expressions:

1. log54:
This expression represents the logarithm of 54 to an unspecified base. If no base is mentioned, it is usually assumed to be 10 (logarithm with base 10).

So, log54 would yield the exponent y to which 10 needs to be raised to obtain 54. In other words, 10^y = 54.

To find the value of log54, we can use the natural logarithm, which has a base of e. We can rewrite the equation as ln(10^y) = ln(54).
Since the natural logarithm (ln) is the inverse of the exponential function, e^ln(10^y) = e^ln(54). The left side simplifies to 10^y.

Therefore, we can rewrite the equation as 10^y = 54. We need to solve for y.
By testing various values of y, we find that 10^1.732 ≈ 54. Therefore, log54 ≈ 1.732.

2. log24:
Similar to the previous example, we have an unspecified base. Assuming the base to be 10, we need to solve for y in the equation 10^y = 24.

Through trial and error, we can find that 10^1.38 ≈ 24. Hence, log24 ≈ 1.38.

3. log0.8:
Again, assuming base 10, we need to determine the exponent y in 10^y = 0.8.

In this case, the number is less than 1, so the logarithm will be negative. By experimenting with different values, we can see that 10^(-0.0969) ≈ 0.8. Therefore, log0.8 ≈ -0.0969.

So, the approximate values of log54, log24, and log0.8 are 1.732, 1.38, and -0.0969, respectively.