How do I express these in scientific notation AND Log10 form?

1) ln(8.1)
2) 32.8 x 10^-2 + 3.15 x 10^-1
3) 10^-2 x 10^4.5
4) 10^-45
5) 8^2.34

I will be happy to critique your work here. Most of these require conversion. Do the math, and let your calculator do the log10 form.

If I knew how to do the math, I wouldn't have asked for help.

This not really a response. I need help in translating a notation for viral load, for example 5.2log10. What does this mean?

No problem! I'll guide you through the steps to express these expressions in scientific notation and Log10 form.

1) ln(8.1):
To express this in scientific notation, you'll need to compute the natural logarithm of 8.1 and then convert it to scientific notation. Since the natural logarithm is a mathematical operation and not a multiplication, it doesn't have a Log10 form. However, we can still compute its value using either a calculator or logarithm tables.

Using a calculator, the value of ln(8.1) is approximately 2.092.
To convert it to scientific notation, we can write it as 2.092 x 10^0.

2) 32.8 x 10^-2 + 3.15 x 10^-1:
To express this expression in scientific notation, we first need to simplify it.

32.8 x 10^-2 = 0.328
3.15 x 10^-1 = 0.315
Adding these simplified values, we get 0.328 + 0.315 = 0.643.

To write this in scientific notation, we need to convert it to the form a x 10^b, where a is a number between 1 and 10 (inclusive).

0.643 = 6.43 x 10^-1.

For the Log10 form, we simply need to use a calculator to find Log10(0.643). The value is approximately -0.190.

3) 10^-2 x 10^4.5:
To simplify this expression, we can add the exponents to get:

10^(-2 + 4.5) = 10^2.5

To express this in scientific notation, we can write it as 3.162 x 10^2.

For the Log10 form, we can use a calculator to find Log10(3.162). The value is approximately 0.500.

Note that Log10(10^2.5) is simply 2.5.

4) 10^-45:
This expression is already in scientific notation. It can be written as 1 x 10^-45.

For the Log10 form, we can calculate Log10(10^-45) using a calculator. The value is equal to -45.

5) 8^2.34:
To evaluate this expression, you can use a calculator or a computer program as it involves exponentiation.

Using a calculator, the value of 8^2.34 is approximately 54.058.

To express this in scientific notation, we can write it as 5.406 x 10^1.

For the Log10 form, we can calculate Log10(54.058) using a calculator, which is approximately 1.732.

I hope these explanations help! Let me know if you have any further questions or if you'd like me to clarify anything.