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
Please show some effort, and please stop posting under multiple names.
To express the given expressions in scientific notation and log base 10 form, we'll break down each expression and convert them accordingly:
1) ln(8.1):
- Scientific notation: The natural logarithm, ln(x), cannot be expressed directly in scientific notation. The output of ln(8.1) is simply a numerical value and not a product involving a power of ten.
- Log base 10: To express ln(8.1) in log base 10 form, we can use the identity ln(x) = log base 10 (x) / log base 10 (e). By dividing ln(8.1) by ln(e) (around 2.303), we can obtain the log base 10 form of the expression.
2) 32.8 x 10^-2 + 3.15 x 10^-1:
- Scientific notation: The given expression is already in scientific notation form, where the coefficients are multiplied by powers of ten. To perform the addition, we need to ensure that both terms have the same power of ten.
32.8 x 10^-2 + 3.15 x 10^-1 = (32.8 x 10^-2) + (0.315 x 10^0) = (3.28 x 10^-1) + (3.15 x 10^-1) = 6.43 x 10^-1
- Log base 10: To express 6.43 x 10^-1 in log base 10 form, we can write it as log base 10 (6.43) - 1.
3) 10^-2 x 10^4.5:
- Scientific notation: When multiplying numbers with the same base, we add their exponents. In this case, 10^-2 * 10^4.5 = 10^(4.5 - 2) = 10^2.5.
- Log base 10: To express 10^2.5 in log base 10 form, we can simply write it as log base 10 (10) * 2.5 = 2.5.
4) 10^-45:
- Scientific notation: The given expression is already in scientific notation form.
- Log base 10: To express 10^-45 in log base 10 form, we can write it as log base 10 (10) * -45 = -45.
5) 8^2.34:
- Scientific notation: This expression does not involve a power of ten, so it cannot be expressed in scientific notation.
- Log base 10: To express 8^2.34 in log base 10 form, we can use the property log base b (x^y) = y * log base b (x). In this case, it would be approximately 2.34 * log base 10 (8).
Remember, scientific notation is useful for expressing numbers that are extremely large or small, while log base 10 form helps in representing numbers as exponents with a base of 10.